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Gaugino Condensation
In quantum field theory, gaugino condensation is the nonzero vacuum expectation value in some models of a bilinear expression constructed in theories with supersymmetry from the superpartner of a gauge boson called the gaugino. The gaugino and the bosonic gauge field and the D-term are all components of a supersymmetric vector superfield in the Wess–Zumino gauge. : \langle \lambda^a_\alpha \lambda^b_\beta\rangle \sim \delta^\epsilon_\Lambda^3 where \lambda represents the gaugino field (a spinor) and \Lambda is an energy scale, and represent Lie algebra indices and and represent van der Waerden (two component spinor) indices. The mechanism is somewhat analogous to chiral symmetry breaking and is an example of a fermionic condensate. In the superfield notation, W_\alpha \equiv \overline^2 D_\alpha V is the gauge field strength and is a chiral superfield. : \langle W^a_\alpha W^b_\beta \rangle = \langle \lambda^a_\alpha \lambda^b_\beta\rangle \sim \delta^\epsilon_\Lambda^3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spinor
In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. Unlike vectors and tensors, a spinor transforms to its negative when the space is continuously rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors: spinors can be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential forms). It is also possible to associate a substantially similar notion of spinor to Minkowski space, in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tachyon Condensation
A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist they could be used to send signals faster than light. According to the theory of relativity this would violate causality, leading to logical paradoxes such as the grandfather paradox. Tachyons would exhibit the unusual property of increasing in speed as their energy decreases, and would require infinite energy to slow down to the speed of light. No verifiable experimental evidence for the existence of such particles has been found. In the 1967 paper that coined the term, Gerald Feinberg proposed that tachyonic particles could be made from excitations of a quantum field with imaginary mass. However, it was soon realized that Feinberg's model did not in fact allow for superluminal (faster-than-light) particles or signals a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R-symmetry
In theoretical physics, the R-symmetry is the symmetry transforming different supercharges in a theory with supersymmetry into each other. In the simplest case of the ''N''=1 supersymmetry, such an R-symmetry is isomorphic to a global U(1) group or its discrete subgroup (for the Z2 subgroup it is called R-parity). For extended supersymmetry, the R-symmetry group becomes a global U(N) non-abelian group In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (''G'', ∗) in which there exists at least one pair of elements ''a'' and ''b'' of ''G'', such that ''a'' ∗ ' .... In a model that is classically invariant under both ''N''=1 supersymmetry and conformal transformations, the closure of the superconformal algebra (at least on-shell) needs the introduction of a further bosonic generator that is associated to the R-symmetry. References * Supersymmetry {{quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-term
In theoretical physics, one often analyzes theories with supersymmetry in which F-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a superspace. This superspace involves four extra fermionic coordinates \theta^1,\theta^2,\bar\theta^1,\bar\theta^2, transforming as a two-component spinor and its conjugate. Every superfield—i.e. a field that depends on all coordinates of the superspace—may be expanded with respect to the new fermionic coordinates. There exists a special kind of superfields, the so-called chiral superfields, that only depend on the variables \theta but not their conjugates. The last term in the corresponding expansion, namely F \theta^1\theta^2, is called the F-term. Applying an infinitesimal supersymmetry transformation to a chiral superfield results in yet another chiral superfield whose F-term, in particular, changes by a total derivative. This is significant because then \int is invariant under SUSY transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Superfield
In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra. Then a superfield is a field on superspace which is valued in such a representation. Naïvely, or when considering flat superspace, a superfield can simply be viewed as a function on superspace. Formally, it is a section of an associated supermultiplet bundle. Phenomenologically, superfields are used to describe particles. It is a feature of supersymmetric field theories that particles form pairs, called superpartners where bosons are paired with fermions. These supersymmetric fields are used to build supersymmetric quantum field theories, where the fields are promoted to operators. History Superfields were introduced by Abdus Salam and J. A. Strathdee in their 1974 articlSupergauge Transformations Operations on superfields and a partial classification were presented a few months later by Sergio Ferrara, Julius Wess and Bruno Zumino iSupergauge Multiplets and Superfields Naming and cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermionic Condensate
A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar conditions. The earliest recognized fermionic condensate described the state of electrons in a superconductor; the physics of other examples including recent work with fermionic atoms is analogous. The first atomic fermionic condensate was created by a team led by Deborah S. Jin using potassium-40 atoms at the University of Colorado Boulder in 2003. Background Superfluidity Fermionic condensates are attained at lower temperatures than Bose–Einstein condensates. Fermionic condensates are a type of superfluid. As the name suggests, a superfluid possesses fluid properties similar to those possessed by ordinary liquids and gases, such as the lack of a definite shape and the ability to flow in response to applied forces. However, superfluids pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry Breaking
In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awarded the 2008 Nobel prize in physics for describing this phenomenon ("for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"). Overview Quantum chromodynamics Experimentally, it is observed that the masses of the octet of pseudoscalar mesons (such as the pion) are much lighter than the next heavier states such as the octet of vector mesons, such as rho meson. This is a consequence of spontaneous symmetry breaking of chiral symmetry in a fermion sector of QCD with 3 flavors of light quarks, , , and . Such a theory, for idealized massless quarks, has global chiral flavor symmetry. Under SSB, this is spontaneously broken to the diagonal flavor ''SU''(3) subgroup, generating eight Nambu–Goldstone bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waerden Notation
In theoretical physics, Van der Waerden notation refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard in twistor theory and supersymmetry. It is named after Bartel Leendert van der Waerden. Dotted indices ;Undotted indices (chiral indices) Spinors with lower undotted indices have a left-handed chirality, and are called chiral indices. :\Sigma_\mathrm = \begin \psi_\\ 0 \end ;Dotted indices (anti-chiral indices) Spinors with raised dotted indices, plus an overbar on the symbol (not index), are right-handed, and called anti-chiral indices. :\Sigma_\mathrm = \begin 0 \\ \bar^\\ \end Without the indices, i.e. "index free notation", an overbar is retained on right-handed spinor, since ambiguity arises between chirality when no index is indicated. Hatted indices Indices which have hats are called Dirac indices, and are the set of dotted and undotted, or chiral and anti-chiral, indices. For example, if : \alpha = 1,2\,,\d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wess–Zumino Gauge
In particle physics, the Wess–Zumino gauge is a particular choice of a gauge transformation in a gauge theory with supersymmetry. In this gauge, the supersymmetrized gauge transformation is chosen in such a way that most components of the vector superfield vanish, except for the usual physical ones when the function of the superspace is expanded in terms of components. See also * Supersymmetric gauge theory In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetry, gauge symmetries. Supersymmetric gauge theory generalizes this notion. Gauge theory A gauge theory is a mathematical framework fo ... Supersymmetric quantum field theory Gauge theories {{quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Expectation Value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are: *The Higgs field has a vacuum expectation value of 246 GeV. This nonzero value underlies the Higgs mechanism of the Standard Model. This value is given by v = 1/\sqrt = 2M_W/g \approx 246.22\, \rm, where ''MW'' is the mass of the W Boson, G_F^0 the reduced Fermi constant, and the weak isospin coupling, in natural units. It is also near the limit of the most massive nuclei, at v = 264.3 Da. *The chiral condensate in quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Superfield
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion. Gauge theory A gauge theory is a mathematical framework for analysing gauge symmetries. There are two types of symmetries, viz., global and local. A global symmetry is the symmetry which remains invariant at each point of a manifold (manifold can be either of spacetime coordinates or that of internal quantum numbers). A local symmetry is the symmetry which depends upon the space over which it is defined, and changes with the variation in coordinates. Thus, such symmetry is invariant only locally (i.e., in a neighborhood on the manifold). Quantum chromodynamics and quantum electrodynamics are famous examples of gauge theories. Supersymmetry In particle physics, there exist particles with two kinds of particle statistics, bosons and fermions. Bosons carry integer spin values, and are characterized by the abil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
