Higgs mechanism

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons would be considered massless, but measurements show that the W+, W−, Z bosons have large masses of around 80 GeV/c2; the Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field that permeates all space to the Standard Model. Below some high temperature, the field causes spontaneous symmetry breaking during interactions; the breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers to the generation of masses for the W±, Z weak gauge bosons through electroweak symmetry breaking; the Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it likely that the field, or one like it, explaining how the Higgs mechanism takes place in nature.

The mechanism was proposed in 1962 by Philip Warren Anderson, following work in the late 1950s on symmetry breaking in superconductivity and a 1960 paper by Yoichiro Nambu that discussed its application within particle physics. A theory able to explain mass generation without "breaking" gauge theory was published simultaneously by three independent groups in 1964: by Robert Brout and François Englert; the Higgs mechanism is therefore called the Brout-Englert-Higgs mechanism, or Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, Anderson-Higgs mechanism, Anderson-Higgs-Kibble mechanism, Higgs-Kibble mechanism by Abdus Salam and ABEGHHK'tH mechanism by Peter Higgs. On 8 October 2013, following the discovery at CERN's Large Hadron Collider of a new particle that appeared to be the long-sought Higgs boson predicted by the theory, it was announced that Peter Higgs and François Englert had been awarded the 2013 Nobel Prize in Physics; the Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, is an essential part of the standard model.

In the standard model, at temperatures high enough that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature, the Higgs field becomes tachyonic. In the standard model, the Higgs field is an SU doublet, a scalar under Lorentz transformations, its electric charge is zero. Under U rotations, it is multiplied by a phase, which thus mixes the real and imaginary parts of the complex spinor into each other, combining to the standard two-component complex representation of the group U; the Higgs field, through the interactions specified by its potential, induces spontaneous breaking of three out of the four generators of the gauge group U. This is written as SU × U, because the diagonal phase factor acts on other fields – quarks in particular. Three out of its four components would ordinarily resolve as Goldstone bosons, if they were not coupled to gauge fields. However, after symmetry breaking, these three of the four degrees of freedom in the Higgs field mix with the three W and Z bosons, are only observable as components of these weak bosons, which are made massive by their inclusion.

The gauge group of the electroweak part of the standard model is SU × U. The group SU is the group of all 2-by-2 unitary matrices with unit determinant. Rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor; the generators for rotations about the x, y, z axes are by half the Pauli matrices σx, σy, σz, so that a rotation of angle θ about the z-axis takes the vacuum to. While the Tx and Ty generators mix up the top and bottom components of the spinor, the Tz rotations only multiply each by opposite phases; this phase can be undone by a U rotation of angle 1/2θ. Under both an SU Tz-rotation and a U rotation by an amount 1/2θ, the vacuum is invariant; this combination of generators Q = T z + 1 2 Y defines the unbroken part of the gauge group, where Q is the electric charge, Tz is the generator of rotations around the z-axis in the SU and Y is the hypercharge generator of the U. This combination of generators (a z rotation in the SU and a simultaneous U rotation by half the angl

Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize and predict natural phenomena. This is in contrast to experimental physics; the advancement of science depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous aether. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect an experimental result lacking a theoretical formulation. A physical theory is a model of physical events, it is judged by the extent. The quality of a physical theory is judged on its ability to make new predictions which can be verified by new observations.

A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results without deep physical understanding.

"Modelers" appear much like phenomenologists, but try to model speculative theories that have certain desirable features, or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories, because developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, reinterpret or generalise extant theories, or create new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled. Theoretical problems that need computational investigation are the concern of computational physics. Theoretical advances may consist in setting aside old, incorrect paradigms or may be an alternative model that provides answers that are more accurate or that can be more applied. In the latter case, a correspondence principle will be required to recover the known result. Sometimes though, advances may proceed along different paths. For example, an correct theory may need some conceptual or factual revisions.

However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle. Physical theories become accepted if they are able to make correct predictions and no incorrect ones; the theory should have, at least as a secondary objective, a certain economy and elegance, a notion sometimes called "Occam's razor" after the 13th-century English philosopher William of Occam, in which the simpler of two theories that describe the same matter just as adequately is preferred. They are more to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method. Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories. Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, continued by Plato and Aristotle, whose views held sway for a millennium. During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar and rhetoric and of the Quadrivium like arithmetic, geometry and astronomy.

During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon. As the Scientific Revolution gathered pace, the concepts of matter, space and causality began to acquire the form we know today, other sciences spun off from the rubric of natural philosophy, thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe.

Phase transition

The term phase transition is most used to describe transitions between solid and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume; the measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions occur in nature and are used today in many technologies. Examples of phase transitions include: The transitions between the solid and gaseous phases of a single component, due to the effects of temperature and/or pressure: A eutectic transformation, in which a two component single phase liquid is cooled and transforms into two solid phases.

The same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid is heated and transforms into a solid phase and a liquid phase. A spinodal decomposition, in which a single phase is cooled and separates into two different compositions of that same phase. Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases; the transition between the ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide; the martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the crystallographic structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides.

The dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron. The emergence of superconductivity in certain metals and ceramics when cooled below a critical temperature; the transition between different molecular structures of solids, such as between an amorphous structure and a crystal structure, between two different crystal structures, or between two amorphous structures. Quantum condensation of bosonic fluids; the superfluid transition in liquid helium is an example of this. The breaking of symmetries in the laws of physics during the early history of the universe as its temperature cooled. Isotope fractionation occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes; when water vapor condenses, the heavier water isotopes become enriched in the liquid phase while the lighter isotopes tend toward the vapor phase. Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables.

This condition stems from the interactions of a large number of particles in a system, does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, topological phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks. At the phase transition point the two phases of a substance and vapor, have identical free energies and therefore are likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred, it is sometimes possible to change the state of a system diabatically in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e. less stable than the phase to which the transition would have occurred, but not unstable either.

This occurs in superheating and supersaturation, for example. Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy, discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable; the various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, the first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative but exhibit discontinuity in a second derivative of the free energy; these include the ferromagnetic phase transition in materials such as iron, where the magnetization, the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature.

The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification sche

String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force, thus string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, condensed matter physics, it has stimulated a number of major developments in pure mathematics; because string theory provides a unified description of gravity and particle physics, it is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter.

Despite much work on these problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of its details. String theory was first studied in the late 1960s as a theory of the strong nuclear force, before being abandoned in favor of quantum chromodynamics. Subsequently, it was realized that the properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity; the earliest version of string theory, bosonic string theory, incorporated only the class of particles known as bosons. It developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in eleven dimensions known as M-theory. In late 1997, theorists discovered an important relationship called the AdS/CFT correspondence, which relates string theory to another type of physical theory called a quantum field theory.

One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. Another issue is that the theory is thought to describe an enormous landscape of possible universes, this has complicated efforts to develop theories of particle physics based on string theory; these issues have led some in the community to criticize these approaches to physics and question the value of continued research on string theory unification. In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics; the first is Albert Einstein's general theory of relativity, a theory that explains the force of gravity and the structure of space and time. The other is quantum mechanics, a different formulation to describe physical phenomena using the known probability principles. By the late 1970s, these two frameworks had proven to be sufficient to explain most of the observed features of the universe, from elementary particles to atoms to the evolution of stars and the universe as a whole.

In spite of these successes, there are still many problems. One of the deepest problems in modern physics is the problem of quantum gravity; the general theory of relativity is formulated within the framework of classical physics, whereas the other fundamental forces are described within the framework of quantum mechanics. A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity. In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of atomic nuclei, black holes, the early universe. String theory is a theoretical framework that attempts to address many others; the starting point for string theory is the idea that the point-like particles of particle physics can be modeled as one-dimensional objects called strings. String theory describes how strings propagate through interact with each other.

In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, it can vibrate in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass and other properties determined by the vibrational state of the string. In this way, all of the different elementary particles may be viewed as vibrating strings. In string theory, one of the vibrational states of the string gives rise to the graviton, a quantum mechanical particle that carries gravitational force, thus string theory is a theory of quantum gravity. One of the main developments of the past several decades in string theory was the discovery of certain "dualities", mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as M-theory.

Studies of string theory have yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, work on string theory