REPRESENTATION OF SPACE INVERSION, TIME REVERSAL, AND PARTICLE CONJUGATION IN QUANTUM FIELD THEORY

1961 ◽  
Vol 39 (1) ◽  
pp. 22-34 ◽  
Author(s):  
F. A. Kaempffer
Keyword(s):  
Time Reversal ◽  
Bilinear Forms ◽  
Fermion Field ◽  
Unitary Operators ◽  
Inversion Time ◽  
Direct Sum ◽  
Representation Of Space ◽  
Antiunitary Operator ◽  
Symmetry Operations ◽  
Space Inversion

The unitary operators of space inversion and particle conjugation and the unitary factor of the antiunitary operator of time reversal can each be written in the form eiΩ, where Ω is the direct sum of two terms, Q = Ω1θ1 + Ω2θ2, with Ω1, Ω2 Hermitean bilinear forms in the creation and annihilation operators of the boson or fermion field under consideration, and θ1 θ2 singular operators which separate the appropriate half spaces needed for the formulation of the symmetry operations. Explicit expressions are given for the generators Ω in case of a non-Hermitean boson field of spin 0, and in case of a four-component fermion field of spin [Formula: see text].

scholarly journals Nonsingular bilinear forms on direct sums of ideals

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Beata Rothkegel
Keyword(s):  
Bilinear Form ◽  
Dedekind Domain ◽  
Bilinear Forms ◽  
Direct Sums ◽  
Direct Sum

AbstractIn the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.

scholarly journals Nonreciprocal transport in gate-induced polar superconductor SrTiO3

2020 ◽  
Vol 6 (13) ◽  
pp. eaay9120 ◽  
Author(s):  
Yuki M. Itahashi ◽  
Toshiya Ideue ◽  
Yu Saito ◽  
Sunao Shimizu ◽  
Takumi Ouchi ◽  
...  
Keyword(s):  
Quantum Transport ◽  
Time Reversal ◽  
Microscopic Theory ◽  
Orbit Interaction ◽  
Inversion Symmetry ◽  
Critical Temperatures ◽  
Rectification Effect ◽  
Inversion Time ◽  
Crossover Behavior ◽  
Polar Symmetry

Polar conductors/superconductors with Rashba-type spin-orbit interaction are potential material platforms for quantum transport and spintronic functionalities. One of their inherent properties is the nonreciprocal transport, where the rightward and leftward currents become inequivalent, reflecting spatial inversion/time-reversal symmetry breaking. Such a rectification effect originating from the polar symmetry has been recently observed at interfaces or bulk Rashba semiconductors, while its mechanism in a polar superconductor remains elusive. Here, we report the nonreciprocal transport in gate-induced two-dimensional superconductor SrTiO3, which is a Rashba superconductor candidate. In addition to the gigantic enhancement of nonreciprocal signals in the superconducting fluctuation region, we found kink and sharp peak structures around critical temperatures, which reflect the crossover behavior from the paraconductivity origin to the vortex origin, based on a microscopic theory. The present result proves that the nonreciprocal transport is a powerful tool for investigating the interfacial/polar superconductors without inversion symmetry, where rich exotic features are theoretically prognosticated.

The structure of unitary actions of finitely generated nilpotent groups

2000 ◽  
Vol 20 (3) ◽  
pp. 809-820 ◽  
Author(s):  
A. LEIBMAN
Keyword(s):  
Hilbert Space ◽  
Nilpotent Group ◽  
Continuous Spectrum ◽  
Nilpotent Groups ◽  
Unitary Operators ◽  
Finitely Generated ◽  
Direct Sum

Let $G$ be a finitely generated nilpotent group of unitary operators on a Hilbert space ${\cal H}$. We prove that ${\cal H}$ is decomposable into a direct sum ${\cal H}=\bigoplus_{\alpha\in A}{\cal L}_{\alpha}$ of pairwise orthogonal closed subspaces so that elements of $G$ permute the subspaces ${\cal L}_{\alpha}$, and if $T({\cal L}_{\alpha})={\cal L}_{\alpha}$, then the action of $T$ on ${\cal L}_{\alpha}$ is either scalar or has continuous spectrum. We also provide examples showing that analogous results do not hold for solvable non-nilpotent groups.

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