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Projective Superspace
In supersymmetry, a theory of particle physics, projective superspace is one way of dealing with \mathcal=2 supersymmetric theories, i.e. with 8 real SUSY generators, in a manifestly covariant manner. See also * Superspace * Harmonic superspace In supersymmetry, harmonic superspace is one way of dealing with supersymmetric theories with 8 real SUSY generators in a manifestly covariant manner. It turns out that the 8 real SUSY generators are pseudoreal, and after complexification, corres ... References * Supersymmetry {{Quantum-stub ...
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Supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which the equations for force and the equations for matter are identical. In theoretical physics, theoretical and mathematical physics, any theory with this property has the ''principle of supersymmetry'' (SUSY). Dozens of supersymmetric theories exist. In theory, supersymmetry is a type of Spacetime symmetries, spacetime symmetry betwe ...
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Particle Physics
Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the study of combinations of protons and neutrons is called nuclear physics. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three Generation (particle physics), generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of Up quark, up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quark, Quarks cannot exist on their own but form hadrons. Hadrons that ...
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SUSY Generator
Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which 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. In theory, supersymmetry is a type of spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and fo ...
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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 extend ...
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Harmonic Superspace
In supersymmetry, harmonic superspace is one way of dealing with supersymmetric theories with 8 real SUSY generators in a manifestly covariant manner. It turns out that the 8 real SUSY generators are pseudoreal, and after complexification, correspond to the tensor product of a four-dimensional Dirac spinor with the fundamental representation of SU(2)R. The quotient space SU(2)_R/U(1)_R \approx S^2 \simeq \mathbb^1, which is a 2-sphere/Riemann sphere. Harmonic superspace describes N=2 D=4, N=1 D=5, and N=(1,0) D=6 SUSY in a manifestly covariant manner. There are many possible coordinate systems over S2, but the one chosen not only involves redundant coordinates, but also happen to be a coordinatization of SU(2)_R \approx S^3. We only get S2 ''after'' a projection over U(1)_R \approx S^1. This is of course the Hopf fibration. Consider the left action of SU(2)R upon itself. We can then extend this to the space of complex valued smooth functions over SU(2)R. In particular, we have ...
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Journal Of Physics A
The ''Journal of Physics A: Mathematical and Theoretical'' is a peer-reviewed scientific journal published by IOP Publishing, the publishing branch of the Institute of Physics. It is part of the '' Journal of Physics'' series and covers theoretical physics focusing on sophisticated mathematical and computational techniques. The journal is divided into six sections covering: statistical physics; chaotic and complex systems; mathematical physics; quantum mechanics and quantum information theory; classical and quantum field theory; fluid and plasma theory. The editor in chief is Joseph A Minahan ( Uppsala Universitet, Sweden). According to the ''Journal Citation Reports'', the journal has a 2023 impact factor of 2.0. History ''Journal of Physics A'' was established in 1968 as one of the subdivisions of the earlier title, '' Proceedings of the Physical Society'', established in 1874, the flagship journal of the Physical Society of London. The Physical Society later became the In ...
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