scholarly journals Restricted Weyl symmetry

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Ichiro Oda
Keyword(s):  
Weyl Symmetry

scholarly journals Weyl symmetry inspired inflation and dark matter

2020 ◽  
Vol 803 ◽  
pp. 135320 ◽  
Author(s):  
Yong Tang ◽  
Yue-Liang Wu
Keyword(s):  
Dark Matter ◽  
Weyl Symmetry

scholarly journals SUPER-τ3QED AND THE DIMENSIONAL REDUCTION OF N=1SUPER-QED2+2

1996 ◽  
Vol 11 (08) ◽  
pp. 1367-1389 ◽  
Author(s):  
M.A. DE ANDRADE ◽  
O.M. DEL CIMA
Keyword(s):  
Vector Field ◽  
Imaginary Part ◽  
Gauge Invariance ◽  
Dimensional Reduction ◽  
Complex Vector ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Supersymmetric Version ◽  
Supersymmetric Gauge ◽  
Weyl Symmetry

In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .

scholarly journals SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1099 ◽  
Author(s):  
Peter Adam ◽  
Vladimir A. Andreev ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko ◽  
Matyas Mechler
Keyword(s):  
Probability Distributions ◽  
Star Product ◽  
Kinetic Equations ◽  
Random Variables ◽  
Continuous Variables ◽  
Probability Representation ◽  
Density Operators ◽  
Symmetry Properties ◽  
Weyl Symmetry ◽  
Qubit States

In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties.

scholarly journals Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

2021 ◽  
Vol 36 (28) ◽  
pp. 2150203
Author(s):  
Ichiro Oda
Keyword(s):  
Conformal Symmetry ◽  
Goldstone Boson ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Global Scale ◽  
Special Conformal Transformation ◽  
Symmetry Breakdown ◽  
Weyl Symmetry ◽  
Spontaneous Symmetry Breakdown

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

scholarly journals Residual Weyl symmetry out of conformal geometry and its BRST structure

2015 ◽  
Vol 2015 (9) ◽  
Author(s):  
J. François ◽  
S. Lazzarini ◽  
T. Masson
Keyword(s):  
Conformal Geometry ◽  
Weyl Symmetry

scholarly journals Inflation as a spontaneous symmetry breaking of Weyl symmetry

2019 ◽  
Vol 2019 (01) ◽  
pp. 022-022 ◽  
Author(s):  
Alexander Barnaveli ◽  
Stefano Lucat ◽  
Tomislav Prokopec
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Weyl Symmetry

scholarly journals Selected topics in scalar–tensor theories and beyond

2019 ◽  
Vol 28 (07) ◽  
pp. 1930012 ◽  
Author(s):  
Israel Quiros
Keyword(s):  
Theoretical Perspective ◽  
Scalar Fields ◽  
Theory Of Relativity ◽  
Postgraduate Students ◽  
Higher Derivative ◽  
Long Time ◽  
Theories Of Gravity ◽  
Weyl Symmetry ◽  
Stability Issues ◽  
First Time

Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time, these escaped detection until 2012 when the Higgs boson was observed for the first time. Since then, alternatives to the general theory of relativity like the Brans–Dicke (BD) theory, scalar–tensor theories of gravity and their higher derivative generalizations — collectively known as Horndeski theories — have acquired renewed interest. In the present review, we discuss several selected topics regarding these theories, mainly from the theoretical perspective but with due mention of the observational aspect. Among the topics covered in this review, we pay special attention to the following: (1) the asymptotic dynamics of cosmological models based on the BD, scalar–tensor and Horndeski theories, (2) inflationary models, extended quintessence and the Galileons, with emphasis in causality and stability issues, (3) the chameleon and Vainshtein screening mechanisms that may allow the elusive scalar field to evade the tight observational constraints implied by the solar system experiments, (4) the conformal frames conundrum with a brief discussion on the disformal transformations and (5) the role of Weyl symmetry and scale invariance in the gravitation theories. The review is aimed at specialists as well as at nonspecialists in the subject, including postgraduate students.

scholarly journals Quadratic gravity and restricted Weyl symmetry

2021 ◽  
pp. 2150139
Author(s):  
Arata Kamimura ◽  
Ichiro Oda
Keyword(s):  
Gauge Symmetry ◽  
Degrees Of Freedom ◽  
Minkowski Spacetime ◽  
Static Condition ◽  
Gauge Parameter ◽  
Zero Energy ◽  
Quadratic Gravity ◽  
Weyl Symmetry ◽  
Dynamical Degrees ◽  
The Relationship

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

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