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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 ...
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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 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 characterize ...
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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 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 characterize ...
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Superspace
Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions ''x'', ''y'', ''z'', ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom. The word "superspace" was first used by John Archibald Wheeler, John Wheeler in an unrelated sense to describe the Configuration space (physics), configuration space of general relativity; for example, this usage may be seen in his 1973 textbook ''Gravitation (book), Gravitation''. Informal discussion There are several similar, but not equivalent, definitions of superspace that have been used, and continue to be used in the mathematical and physics literature. One such usage is as a synonym for super Minkowski space. In this case, one takes ordinary Minkowski space, and extends ...
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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 ...
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D-term
In theoretical physics, one often analyzes theories with supersymmetry in which D-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. The generic kind of superfields, typically a vector superfield, indeed depend on all these coordinates. The last term in the corresponding expansion, namely D \theta^1\theta^2\bar\theta^1\bar\theta^2, is called the D-term. Manifestly supersymmetric Lagrangians may also be written as integrals over the whole superspace. Some special terms, such as the superpotential, may be written as integrals over \thetas only, which are known as F-terms, and should be contrasted with the present D-term ...
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Auxiliary Field
In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field A contains an algebraic quadratic term and an arbitrary linear term, while it contains no kinetic terms (derivatives of the field): :\mathcal_\text = \frac(A, A) + (f(\varphi), A). The equation of motion for A is :A(\varphi) = -f(\varphi), and the Lagrangian becomes :\mathcal_\text = -\frac(f(\varphi), f(\varphi)). Auxiliary fields generally do not propagate, and hence the content of any theory can remain unchanged in many circumstances by adding such fields by hand. If we have an initial Lagrangian \mathcal_0 describing a field \varphi, then the Lagrangian describing both fields is :\mathcal = \mathcal_0(\varphi) + \mathcal_\text = \mathcal_0(\varphi) - \frac\big(f(\varphi), f(\varphi)\big). Therefore, auxiliary fields can be employed to cancel quadratic terms in \varphi in \mathcal_0 and linearize the ...
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Sergio Ferrara
Sergio Ferrara (born May 2, 1945) is an Italian physicist working on theoretical physics of elementary particles and mathematical physics. He is renowned for the discovery of theories introducing supersymmetry as a symmetry of elementary particles (super- Yang–Mills theories, together with Bruno Zumino) and of supergravity, the first significant extension of Einstein's general relativity, based on the principle of "local supersymmetry" (together with Daniel Z. Freedman, and Peter van Nieuwenhuizen). He is an emeritus staff member at CERN and a professor emeritus at the University of California, Los Angeles. Career Sergio Ferrara was born on 2 May 1945 in Rome, Italy. He graduated from the University of Rome, obtaining in 1968 the Laurea Degree (the highest Degree that was awarded in Italy at the time). Since then he has worked as a CNEN and INFN researcher at the Frascati National Laboratories; as a CNRS Visiting Scientist at the Laboratoire de Physique Théorique, École N ...
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Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ...
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Abdus Salam
Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Punjabi Pakistani theoretical physicist and a Nobel Prize laureate. He shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for his contribution to the electroweak unification theory. He was the first Pakistani and the first from an Islamic country to receive a Nobel Prize in science and the second from an Islamic country to receive any Nobel Prize, after Anwar Sadat of Egypt. Salam was scientific advisor to the Ministry of Science and Technology in Pakistan from 1960 to 1974, a position from which he played a major and influential role in the development of the country's science infrastructure. Salam contributed to numerous developments in theoretical and particle physics in Pakistan. He was the founding director of the Space and Upper Atmosphere Researc ...
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Scalar Field
In mathematics and physics, a scalar field is a function (mathematics), function associating a single number to every point (geometry), point in a space (mathematics), space – possibly physical space. The scalar may either be a pure Scalar (mathematics), mathematical number (dimensionless) or a scalar (physics), scalar physical quantity (with unit of measurement, units). In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory. Definition Mathematically, a scalar field on a Region (mathematical analysis), region ''U ...
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Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is formed by r ...
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Majorana–Weyl 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 ...
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