Mathematical formulation of the Standard Model
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU × SU × U. The theory is viewed as containing the fundamental set of particles – the leptons, gauge bosons and the Higgs particle; the Standard Model is renormalizable and mathematically self-consistent, however despite having huge and continued successes in providing experimental predictions it does leave some unexplained phenomena. In particular, although the physics of special relativity is incorporated, general relativity is not, the Standard Model will fail at energies or distances where the graviton is expected to emerge. Therefore, in a modern field theory context, it is seen as an effective field theory; this article requires some background in physics and mathematics, but is designed as both an introduction and a reference. The standard model is a quantum field theory, meaning its fundamental objects are quantum fields which are defined at all points in spacetime.
These fields are the fermion fields, ψ, which account for "matter particles". That these are quantum rather than classical fields has the mathematical consequence that they are operator-valued. In particular, values of the fields do not commute; as operators, they act upon the quantum state. The dynamics of the quantum state and the fundamental fields are determined by the Lagrangian density L; this plays a role similar to that of the Schrödinger equation in non-relativistic quantum mechanics, but a Lagrangian is not an equation of motion – rather, it is a polynomial function of the fields and their derivatives, used with the principle of least action. While it would be possible to derive a system of differential equations governing the fields from the Lagrangian, it is more common to use other techniques to compute with quantum field theories; the standard model is furthermore a gauge theory, which means there are degrees of freedom in the mathematical formalism which do not correspond to changes in the physical state.
The gauge group of the standard model is SU × SU × U, where U acts on B and φ, SU acts on W and φ, SU acts on G. The fermion field ψ transforms under these symmetries, although all of them leave some parts of it unchanged. In classical mechanics, the state of a system can be captured by a small set of variables, the dynamics of the system is thus determined by the time evolution of these variables. In classical field theory, the field is part of the state of the system, so in order to describe it one introduces separate variables for every point in spacetime. In quantum mechanics, the classical variables are turned into operators, but these do not capture the state of the system, instead encoded into a wavefunction ψ or more abstract ket vector. If ψ is an eigenstate with respect to an operator P Pψ = λψ for the corresponding eigenvalue λ, hence letting an operator P act on ψ is analogous to multiplying ψ by the value of the classical variable to which P corresponds. By extension, a classical formula where all variables have been replaced by the corresponding operators will behave like an operator which, when it acts upon the state of the system, multiplies it by the analogue of the quantity that the classical formula would compute.
The formula as such does. Quantum fields relate to quantum mechanics as classical fields do to classical mechanics, i.e. there is a separate operator for every point in spacetime, these operators do not carry any information about the state of the system. In particular, the quantum fields are not wavefunctions though the equations which govern their time evolution may be deceptively similar to those of the corresponding wavefunction in a semiclassical formulation. There is no variation in strength of the fields between different points in spacetime. Mathematically it may look as though all of the fields are vector-valued, since they all have several components, can be multiplied by matrices, etc. but physicists assign a more specific physical meaning to the word: a vector is something which transforms like a four-vector under Lorentz transformations, a scalar is something, invariant under Lorentz transformations. The B, Wj, Ga fields are all vectors in this sense, so the corresponding particles are said to be vector bosons.
The Higgs field φ is a scalar. The fermion field ψ does transform under Lorentz transformations. Therefore, these constitute a third kind of quantity, known as a spinor, it is common to make use of abstract index notation for the vector fields, in which case the vector fields all come with a Lorentzian index μ, like so: B μ, W j μ, G
Greece the Hellenic Republic, self-identified and known as Hellas, is a country located in Southern and Southeast Europe, with a population of 11 million as of 2016. Athens is largest city, followed by Thessaloniki. Greece is located at the crossroads of Europe and Africa. Situated on the southern tip of the Balkan Peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, Turkey to the northeast; the Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, the Cretan Sea and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean Basin and the 11th longest coastline in the world at 13,676 km in length, featuring a large number of islands, of which 227 are inhabited. Eighty percent of Greece is mountainous, with Mount Olympus being the highest peak at 2,918 metres; the country consists of nine geographic regions: Macedonia, Central Greece, the Peloponnese, Epirus, the Aegean Islands, Thrace and the Ionian Islands.
Greece is considered the cradle of Western civilisation, being the birthplace of democracy, Western philosophy, Western literature, political science, major scientific and mathematical principles, Western drama and notably the Olympic Games. From the eighth century BC, the Greeks were organised into various independent city-states, known as poleis, which spanned the entire Mediterranean region and the Black Sea. Philip of Macedon united most of the Greek mainland in the fourth century BC, with his son Alexander the Great conquering much of the ancient world, from the eastern Mediterranean to India. Greece was annexed by Rome in the second century BC, becoming an integral part of the Roman Empire and its successor, the Byzantine Empire, in which Greek language and culture were dominant. Rooted in the first century A. D. the Greek Orthodox Church helped shape modern Greek identity and transmitted Greek traditions to the wider Orthodox World. Falling under Ottoman dominion in the mid-15th century, the modern nation state of Greece emerged in 1830 following a war of independence.
Greece's rich historical legacy is reflected by its 18 UNESCO World Heritage Sites. The sovereign state of Greece is a unitary parliamentary republic and developed country with an advanced high-income economy, a high quality of life, a high standard of living. A founding member of the United Nations, Greece was the tenth member to join the European Communities and has been part of the Eurozone since 2001, it is a member of numerous other international institutions, including the Council of Europe, the North Atlantic Treaty Organization, the Organisation for Economic Co-operation and Development, the World Trade Organization, the Organization for Security and Co-operation in Europe, the Organisation internationale de la Francophonie. Greece's unique cultural heritage, large tourism industry, prominent shipping sector and geostrategic importance classify it as a middle power, it is the largest economy in the Balkans. The names for the nation of Greece and the Greek people differ from the names used in other languages and cultures.
The Greek name of the country is Hellas or Ellada, its official name is the Hellenic Republic. In English, the country is called Greece, which comes from Latin Graecia and means'the land of the Greeks'; the earliest evidence of the presence of human ancestors in the southern Balkans, dated to 270,000 BC, is to be found in the Petralona cave, in the Greek province of Macedonia. All three stages of the stone age are represented for example in the Franchthi Cave. Neolithic settlements in Greece, dating from the 7th millennium BC, are the oldest in Europe by several centuries, as Greece lies on the route via which farming spread from the Near East to Europe. Greece is home to the first advanced civilizations in Europe and is considered the birthplace of Western civilisation, beginning with the Cycladic civilization on the islands of the Aegean Sea at around 3200 BC, the Minoan civilization in Crete, the Mycenaean civilization on the mainland; these civilizations possessed writing, the Minoans writing in an undeciphered script known as Linear A, the Mycenaeans in Linear B, an early form of Greek.
The Mycenaeans absorbed the Minoans, but collapsed violently around 1200 BC, during a time of regional upheaval known as the Bronze Age collapse. This ushered from which written records are absent. Though the unearthed Linear B texts are too fragmentary for the reconstruction of the political landscape and can't support the existence of a larger state contemporary Hittite and Egyptian records suggest the presence of a single state under a "Great King" based in mainland Greece; the end of the Dark Ages is traditionally dated to the year of the first Olympic Games. The Iliad and the Odyssey, the foundational texts of Western literature, are believed to have been composed by Homer in the 7th or 8th centuries BC. With the end of the Dark Ages, there emerged various kingdoms and city-states across the Greek peninsula, which spread to the shores of the Black Sea, So
The European Organization for Nuclear Research, known as CERN, is a European research organization that operates the largest particle physics laboratory in the world. Established in 1954, the organization is based in a northwest suburb of Geneva on the Franco–Swiss border and has 23 member states. Israel is the only non-European country granted full membership. CERN is an official United Nations Observer; the acronym CERN is used to refer to the laboratory, which in 2016 had 2,500 scientific and administrative staff members, hosted about 12,000 users. In the same year, CERN generated 49 petabytes of data. CERN's main function is to provide the particle accelerators and other infrastructure needed for high-energy physics research – as a result, numerous experiments have been constructed at CERN through international collaborations; the main site at Meyrin hosts a large computing facility, used to store and analyse data from experiments, as well as simulate events. Researchers need remote access to these facilities, so the lab has been a major wide area network hub.
CERN is the birthplace of the World Wide Web. The convention establishing CERN was ratified on 29 September 1954 by 12 countries in Western Europe; the acronym CERN represented the French words for Conseil Européen pour la Recherche Nucléaire, a provisional council for building the laboratory, established by 12 European governments in 1952. The acronym was retained for the new laboratory after the provisional council was dissolved though the name changed to the current Organisation Européenne pour la Recherche Nucléaire in 1954. According to Lew Kowarski, a former director of CERN, when the name was changed, the abbreviation could have become the awkward OERN, Werner Heisenberg said that this could "still be CERN if the name is ". CERN's first president was Sir Benjamin Lockspeiser. Edoardo Amaldi was the general secretary of CERN at its early stages when operations were still provisional, while the first Director-General was Felix Bloch; the laboratory was devoted to the study of atomic nuclei, but was soon applied to higher-energy physics, concerned with the study of interactions between subatomic particles.
Therefore, the laboratory operated by CERN is referred to as the European laboratory for particle physics, which better describes the research being performed there. At the sixth session of the CERN Council, which took place in Paris from 29 June - 1 July 1953, the convention establishing the organization was signed, subject to ratification, by 12 states; the convention was ratified by the 12 founding Member States: Belgium, France, the Federal Republic of Germany, Italy, the Netherlands, Sweden, the United Kingdom, Yugoslavia. Several important achievements in particle physics have been made through experiments at CERN, they include: 1973: The discovery of neutral currents in the Gargamelle bubble chamber. In September 2011, CERN attracted media attention when the OPERA Collaboration reported the detection of faster-than-light neutrinos. Further tests showed that the results were flawed due to an incorrectly connected GPS synchronization cable; the 1984 Nobel Prize for Physics was awarded to Carlo Rubbia and Simon van der Meer for the developments that resulted in the discoveries of the W and Z bosons.
The 1992 Nobel Prize for Physics was awarded to CERN staff researcher Georges Charpak "for his invention and development of particle detectors, in particular the multiwire proportional chamber". The 2013 Nobel Prize for Physics was awarded to François Englert and Peter Higgs for the theoretical description of the Higgs mechanism in the year after the Higgs boson was found by CERN experiments; the World Wide Web began as a CERN project named ENQUIRE, initiated by Tim Berners-Lee in 1989 and Robert Cailliau in 1990. Berners-Lee and Cailliau were jointly honoured by the Association for Computing Machinery in 1995 for their contributions to the development of the World Wide Web. Based on the concept of hypertext, the project was intended to facilitate the sharing of information between researchers; the first website was activated in 1991. On 30 April 1993, CERN announced. A copy of the original first webpage, created by Berners-Lee, is still published on the World Wide Web Consortium's website as a historical document.
Prior to the Web's development, CERN had pioneered the introduction of Internet technology, beginning in the early 1980s. More CERN has become a facility for the development of grid computing, hosting projects including the Enabling Grids for E-sciencE and LHC Computing Grid, it hosts the CERN Internet Exchange Point, one of the two main internet exchange points in Switzerland. CERN operates a network of a decelerator; each machine in the chain increases the energy of particle beams before delivering them
Luciano Maiani is a Sammarinese physicist best known for his prediction of the charm quark with Sheldon Lee Glashow and John Iliopoulos. In 1964 Luciano Maiani received his degree in physics and he became a research associate at the Istituto Superiore di Sanità in Italy. During that same year he collaborated with Raoul Gatto's theoretical physics group at the University of Florence, he crossed the Atlantic in 1969 to do a post-doctoral fellowship at Harvard's Lyman Laboratory of Physics. In 1976 Maiani became a professor of theoretical physics at the University of Rome, however he traveled during this period, holding visiting professorships at the Ecole Normale Supérieure of Paris and CERN. Maiani took an interest in the direction of particle physics research start on CERN's Scientific Policy Committee from 1984 to 1991. In 1993, he became president of Italy's Istituto Nazionale di Fisica Nucleare. From 1993 to 1996 Maiani served as a scientific delegate in CERN council and as that council's president in 1997.
Thereafter he became director general of CERN, serving from 1 January 1999 through the end of 2003. From 1995-1997 Maiani chaired Fondo Ricerca Applicata. At the end of 2007 he was proposed as president of Consiglio Nazionale delle Ricerche, but his nomination was suspended temporally after he signed a letter criticizing the rector of'La Sapienza' University in Rome, who invited Pope Benedict XVI to give a lectio magistralis in 2008; however he became the President of CNR since 2008. Luciano Maiani has authored over 100 scientific publications on the theory of elementary particles with several co-authors. In 1970 he predicted the charmed quark in a paper with Glashow and Iliopoulos, discovered at SLAC and Brookhaven in 1974 and led to a Nobel Prize in Physics for the discoverers. Working with Guido Altarelli in 1974 they explained that the observed octet enhancement in weak non-leptonic decays was due to a leading gluon exchange effect in quantum chromodynamics, they extended this effect to describe the weak non-leptonic decays of charm and bottom quarks as well and produced a parton model description of heavy flavor weak decays.
In 1976 Maiani analyzed the CP violation in the six-quark theory and predicted the small electric dipole moment of the neutron. In the 1980s he started using the numerical simulation of lattice QCD and this led to the first prediction of the decay constant of pseudoscalar charmed mesons and of B mesons. A proponent of supersymmetry, Maiani once said that the search for it was "primary goal of modern particle physics", he has not confined his interest to the theoretical side of physics either, with involvement in ALPI, EUROBALL, DAFNE, VIRGO and the LHC. 1979 Matteucci Medal, Accademia Nazionale dei XL 1987 Sakurai Prize of the American Physical Society 1996 Doctor honoris causa, Université de la Méditerranée, Aix-Marseille 2007 Dirac Medal, Abdus Salam International Centre for Theoretical Physics, Italy 2010 Doctor honoris causa, Benemérita Universidad Autónoma de Puebla, Puebla, México GIM mechanism Scientific publications of Luciano Maiani on INSPIRE-HEP
American Physical Society
The American Physical Society is the world's second largest organization of physicists. The Society publishes more than a dozen scientific journals, including the prestigious Physical Review and Physical Review Letters, organizes more than twenty science meetings each year. APS is a member society of the American Institute of Physics; the American Physical Society was founded on May 20, 1899, when thirty-six physicists gathered at Columbia University for that purpose. They proclaimed the mission of the new Society to be "to advance and diffuse the knowledge of physics", in one way or another the APS has been at that task since. In the early years the sole activity of the APS was to hold scientific meetings four per year. In 1913, the APS took over the operation of the Physical Review, founded in 1893 at Cornell University, journal publication became its second major activity; the Physical Review was followed by Reviews of Modern Physics in 1929 and by Physical Review Letters in 1958. Over the years, Phys.
Rev. has subdivided into five separate sections as the fields of physics proliferated and the number of submissions grew. In more recent years, the activities of the Society have broadened considerably. Stimulated by the increase in Federal funding in the period after the Second World War, more by the increased public involvement of scientists in the 1960s, the APS is active in public and governmental affairs, in the international physics community. In addition, the Society conducts extensive programs in education, science outreach, media relations. APS has 11 topical groups covering all areas of physics research. There are 6 forums that reflect the interest of its 50,000 members in broader issues, 9 sections organized by geographical region. In 1999, APS Physics celebrated its centennial with the biggest-ever physics meeting in Atlanta. In 2005, APS took the lead role in United States participation in the World Year of Physics, initiating several programs to broadly publicize physics during the 100th anniversary of Albert Einstein's annus mirabilis.
Einstein@Home, one of the projects APS initiated during World Year of Physics, is an ongoing and popular distributed computing project. During the summer of 2005, the society conducted an electronic poll, in which the majority of APS members preferred the name American Physics Society; the poll became the motivation for a proposal of a name change promised in the leadership election that year. However, because of legal issues, the planned name change was abandoned by the APS Executive Board. To promote public recognition of APS as a physics society, while retaining the name American Physical Society, the APS Executive Board adopted a new logo incorporating the phrase "APS Physics." General use of APS Physics to refer to APS or the American Physical Society is encouraged. The new APS Physics logo was designed by Kerry G. Johnson. Marvin Cohen, APS President, said, "I like the logo. At least now when you are in an elevator at an APS meeting and someone looks at your badge, they won't ask you about sports."
The American Physical Society publishes 13 international research journals and an open-access on-line news and commentary website Physics. Physical Review Letters Reviews of Modern Physics Physical Review A: Atomic and optical physics. Physical Review B: Condensed matter and materials physics. Physical Review C: Nuclear physics. Physical Review D: Particles, fields and cosmology. Physical Review E: Statistical and soft matter physics. Physical Review X: Open access. Physical Review Applied: Experimental and theoretical applications of physics. Physical Review Fluids: Fluid dynamics. Physical Review Accelerators and Beams: Open access. Physical Review Physics Education Research: Open access. Physical Review Materials: A broad-scope international journal for the multidisciplinary community engaged in research on materials. All members of APS receive the monthly publication Physics Today, published by the American Institute of Physics; the Society publishes Inside Science, part of a news service launched in 1999 to place more science stories in the media.
Aimed at both introducing the public to new scientific research and at correcting public misconceptions about science, the publication has editorial independence from APS itself. The American Physical Society has 47 units that represent the wide range of interests of the physics community. Astrophysics Atomic, Molecular & Optical Physics: The objective of the division is the promotion of the fundamental research on atoms, simple molecules and light, their interactions; this is the oldest division of the American Physical Society. It was created in 1943; the division manages a number of prestigious awards for AMO scientists at various stages of their careers, such as the Davisson-Germer Prize in Atomic or Surface Physics, Rabi Prize in AMO Physics, Outstanding Doctoral Thesis Research in AMO Physics, Herbert P. Broida Prize, etc, it organizes annual DAMOP Meetings attended by many leading AMO researchers, both from the United States and abroad. Biological Physics: With over 2,000 members, the division is the second largest learned society in the world devoted to biological physics, following the Biophysical Society.
The objective of the division is the advancement and dissemination of knowledge on the broad interface of physics and biology. This includes st
University of the Mediterranean
The University of the Mediterranean Aix-Marseille II was a French university in the Academy of Aix and Marseille. It was part of the University of Aix-Marseille based across the communes of Aix-en-Provence and Marseille in southern France, it had 24,000 students. On 1 January 2012 it merged with the University of Provence and Paul Cézanne University to become Aix-Marseille University, the youngest, but the largest in terms of students and staff in France; the university is strong in sciences with faculties for science, sport sciences and economic science and management. The medical school comprises the faculties of Medicine and Dentistry. In addition, there are a number of institutes: Institut de Mécanique de Marseille École de Journalisme et de Communication Institut Universitaire de Technologie Institut Régional du Travail Centre d'océanologie de Marseille Ecole Universitaire de Maïeutique Marseille Méditerranée The Université d'Aix-en-Provence was created in 1409 by Louis II de Provence. In 1791, like every university in France, it was dissolved and the faculties were dispersed between the two cities of Aix-en-Provence and Marseille and became autonomous.
On 21 April 1881 by decree of the conseil municipal the medical school was opened at the palais du Pharo by the Vieux Port, Marseille. In 1969, two universities were established between Marseille. In 1973, the third was created. In 1994, the Université d'Aix-Marseille II took the name of Université de la Méditerranée. Xavier Laurent University of Aix-Marseille List of public universities in France by academy Official site