scholarly journals Conformal Symmetry, Accelerated Observers, and Nonlocality

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 978 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
Abelian Subgroup ◽  
Conformal Symmetry ◽  
Minkowski Spacetime ◽  
Conformal Group ◽  
Accelerated Observers ◽  
Spacetime Metric

The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in Minkowski spacetime. The properties of this congruence are studied in order to illustrate the kinematics of accelerated observers in relativistic physics. The generalization of this approach under conformal rescaling of the spacetime metric is examined.

IMPORTED CONFORMAL SYMMETRY OF ANYONS IN A UNIFORM MAGNETIC FIELD

1992 ◽  
Vol 06 (08) ◽  
pp. 1229-1242 ◽  
Author(s):  
T. AWAJI ◽  
M. HOTTA
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
External Magnetic Field ◽  
Uniform Magnetic Field ◽  
Conformal Symmetry ◽  
Dynamical Symmetry ◽  
Conformal Group ◽  
Symmetry Consideration

We analyze an N-body quantum mechanics of anyons in an external magnetic field. It is pointed out that an SO(2, 1) dynamical symmetry, which is related to the conformal group, plays an important role in anyon dynamics. It is shown that the two-body spectrum is fully reproduced solely by the symmetry consideration. Moreover, we discuss some constraints on missing states from the symmetry consideration.

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 THE KERR–SCHILD ANSATZ REVISED

2010 ◽  
Vol 07 (04) ◽  
pp. 693-703 ◽  
Author(s):  
DONATO BINI ◽  
ANDREA GERALICO ◽  
ROY P. KERR
Keyword(s):  
Basic Assumption ◽  
Minkowski Spacetime ◽  
Scalar Function ◽  
Kerr Solution ◽  
Field Equations ◽  
Linear Superposition ◽  
Flat Spacetime ◽  
Linear Perturbations ◽  
Spacetime Metric ◽  
Second Order Equations

Kerr–Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null-vector field, say k, multiplied by some scalar function, say H. The basic assumption which led to Kerr solution was that k be both geodesic and shearfree. This condition is relaxed here and Kerr–Schild Ansatz is revised by treating Kerr–Schild metrics as exact linear perturbations of Minkowski spacetime. The scalar function H is taken as the perturbing function, so that Einstein's field equations are solved order-by-order in powers of H. It turns out that the congruence must be geodesic and shearfree as a consequence of third- and second-order equations, leading to an alternative derivation of Kerr solution.

EXTENDED CONFORMAL GROUP, SUPERSYMMETRY, AND GEOMETRICAL PROPERTIES OF HADRONS

1989 ◽  
Vol 04 (15) ◽  
pp. 3791-3805 ◽  
Author(s):  
PRATUL BANDYOPADHYAY ◽  
PRADIP GHOSH
Keyword(s):  
Lorentz Invariance ◽  
Mass Difference ◽  
Conformal Symmetry ◽  
Symmetry Algebra ◽  
Mass Term ◽  
Discrete Symmetry ◽  
Internal Symmetry ◽  
Conformal Group ◽  
Significant Feature ◽  
Geometrical Properties

We have studied the interrelation among conformal symmetry, internal symmetry and super-symmetry and have shown that extended conformal group which includes, apart from conformal transformation, space, time and conformal reflection can give rise to internal symmetry algebra as well as supersymmetry algebra. To achieve this result, we have dealt with conformal spinors which are taken to be the constituents of the hadrons and these split into two Cartan semispinors or Dirac spinors in the Minkowski space, giving rise to the particle and antiparticle configurations. Supersymmetry is broken here just by the mass term and as such no massless hadron can exist in nature. The internal symmetry arises from the discrete symmetry of reflection. The most significant feature of this formalism is that the symmetry structure helps us to explain the meson-baryon mass difference in an elegant way and the role of fictitious superpartners is completely avoided. Again, any baryon number nonconserving process like proton decay is found to be forbidden by the Lorentz invariance. Finally, it is noted that though the discrete symmetry of reflection is taken to be the origin of the internal symmetry, topological nontrivial structures like strings do not appear here and this also avoids the possibility of the nonconservation of global charge.

scholarly journals FUBINI VACUA AS A CLASSICAL DE SITTER VACUA

2007 ◽  
Vol 22 (29) ◽  
pp. 2217-2235 ◽  
Author(s):  
F. LORAN
Keyword(s):  
Einstein Field Equation ◽  
Minkowski Spacetime ◽  
Vacuum State ◽  
Information Geometry ◽  
Conformal Group ◽  
De Sitter ◽  
Frw Universe ◽  
Scale Invariant ◽  
Scalar Theory ◽  
De Sitter Vacua

The Fubini's idea to introduce a fundamental scale of hadron phenomena by means of dilatation non-invariant vacuum state in the framework of a scale invariant Lagrangian field theory is recalled. The Fubini vacua is invariant under the de Sitter subgroup of the full conformal group. We obtain a finite entropy for the quantum state corresponding to the classical Fubini vacua in Euclidean spacetime resembling the entropy of the de Sitter vacua. In Minkowski spacetime it is shown that the Fubini vacua is mainly a bath of radiation with Rayleigh–Jeans distribution for the low energy radiation. In four dimensions, the critical scalar theory is shown to be equivalent to the Einstein field equation in the ansatz of conformally flat metrics and to the SU(2) Yang–Mills theory in the 't Hooft ansatz. In D dimensions, the Hitchin formula for the information geometry metric of the moduli space of instantons is used to obtain the information geometry of the free-parameter space of the Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant is shown to be given by the coupling constant of the critical scalar theory. In Minkowski spacetime it is shown that the Fubini vacua are equivalent to an open FRW universe.

NONARCHIMEDEAN CONFORMAL FIELD THEORIES

1989 ◽  
Vol 04 (18) ◽  
pp. 4877-4908 ◽  
Author(s):  
EZER MELZER
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Conformal Group ◽  
Field Theories ◽  
Dimensional Euclidean Space ◽  
Conformal Field Theories ◽  
Linear Transformations ◽  
Associative Algebras ◽  
Conformal Field

We present a general formalism for conformal field theories defined on a non-Archimedean field. Such theories are defined by complex-valued correlation functions of fields of a [Formula: see text]-adic variable. Conformal invariance is imposed by requiring the correlation functions to be unchanged under fractional linear transformations, the latter forming the full analogue of the conformal group in two-dimensional, euclidean space-time. All fields in the theory can be taken to be "primary", under the "non-Archimedean conformal group". The conformal symmetry fixes completely the form of all correlation functions, once we are given the weight-spectrum of the theory and the OPE coefficients (which must be the structure constants of certain commutative, associative algebras). We explicitly construct non-Archimedean CFT's having the same weight spectrum as that of Archimedean models of central charge c < 1. The OPE coefficients of these "local" Archimedean and non-Archimedean models are related by adelic formulae.

scholarly journals Conformal quantum mechanics & the integrable spinning Fishnet

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sergey Derkachov ◽  
Enrico Olivucci
Keyword(s):  
Conformal Symmetry ◽  
Scaling Limit ◽  
Principal Series ◽  
Conformal Group ◽  
Baxter Equation ◽  
Special Choice ◽  
Conformal Field ◽  
Quantum Magnet ◽  
Supersymmetric Theories ◽  
Conformal Quantum Mechanics

Abstract In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ,$$ \dot{\ell} $$ ℓ ̇ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆k, ℓk,$$ \dot{\ell} $$ ℓ ̇ k) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed $$ \mathcal{N} $$ N = 4 and $$ \mathcal{N} $$ N = 2 supersymmetric theories.

scholarly journals Non-Lorentzian avatars of (1,0) theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
N. Lambert ◽  
T. Orchard
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Conformal Symmetry ◽  
Minkowski Spacetime ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Superconformal Field Theories ◽  
Conformal Field

Abstract We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1, 3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1, 0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1, 0) conformal field theories.

CLASSICAL YANG-MILLS-DIRAC SYSTEM WITH CONFORMAL SYMMETRY: A GEOMETRICAL ANALYSIS

1994 ◽  
Vol 09 (37) ◽  
pp. 3431-3444 ◽  
Author(s):  
J.-P. ANTOINE ◽  
L. DABROWSKI ◽  
I. MAHARA
Keyword(s):  
Minkowski Space ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Conformal Symmetry ◽  
Conformal Group ◽  
Dirac System ◽  
Geometrical Analysis ◽  
Yang Mills ◽  
Dirac Equations

We consider classical Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under a four-dimensional subgroup of the conformal group. In each of the four different cases that we analyze, the equations admit non-Abelian solutions, but these cannot be obtained analytically. In addition, some cases admit solutions with chiral spinors that may be physically relevant. All these solutions are singular.

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