scholarly journals Structure of Broken Spacetime Symmetries

10.33540/170 ◽  
2020 ◽  
Author(s):  
◽  
Bernardo Finelli de Moraes
Keyword(s):  
Spacetime Symmetries

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

Spacetime symmetries

2001 ◽  
pp. 20-41
Author(s):  
Milutin Blagojević
Keyword(s):  
Spacetime Symmetries

scholarly journals ELEMENTARY PARTICLES AND SPIN REPRESENTATIONS

2004 ◽  
Vol 19 (05) ◽  
pp. 357-362 ◽  
Author(s):  
PAOLO MARANER
Keyword(s):  
Matter Field ◽  
Elementary Particles ◽  
Spacetime Symmetries ◽  
Spin Representation ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Spin Representations ◽  
Theoretical Considerations ◽  
Unified Description

We emphasize that the group-theoretical considerations leading to SO (10) unification of electroweak and strong matter field components naturally extend to spacetime components, providing a truly unified description of all generation degrees of freedoms in terms of a single chiral spin representation of one of the groups SO (13,1), SO (9,5), SO (7,7) or SO (3,11). The realization of these groups as higher-dimensional spacetime symmetries produces unification of all fundamental fermions is a single spacetime spinor.

scholarly journals Spacetime symmetries of the quantum Hall effect

2015 ◽  
Vol 91 (4) ◽  
Author(s):  
Michael Geracie ◽  
Dam Thanh Son ◽  
Chaolun Wu ◽  
Shao-Feng Wu
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Spacetime Symmetries

scholarly journals FERMION DYNAMICS BY INTERNAL AND SPACETIME SYMMETRIES

2009 ◽  
Vol 24 (06) ◽  
pp. 415-427 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Stationary Solutions ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Lorentz Transformations ◽  
Relativistic Limit ◽  
Spinor Structure ◽  
Flat Spacetime ◽  
Fermion Fields

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.

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