scholarly journals Linearized supergravity with a dynamical preferred frame

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Arthur Marakulin ◽  
Sergey Sibiryakov
Keyword(s):  
Lorentz Invariance ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Timelike Vector ◽  
Chiral Vector ◽  
Model Following ◽  
Superluminal Velocity ◽  
General Action ◽  
Spatial Rotations ◽  
Local Lorentz Invariance

Abstract We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether. Embedding aether into a chiral vector superfield, we construct the most general action which describes dynamics of linear perturbations around the Lorentz-violating vacuum and is invariant under the linearized supergravity transformations. The analysis is performed both in the off-shell non-minimal superfield formulation of supergravity and in the “on-shell” approach invoking only physical component fields. The resulting model contains a single free coupling, in addition to the standard supergravity parameters. The spectrum of physical excitations features an enhanced on-shell gravity multiplet comprising four states with helicities 2, 3/2, 3/2 and 1 propagating with superluminal velocity. The remaining excitations propagate with the speed of light. We outline the observational constraints on the model following from its low-energy phenomenology.

scholarly journals SPONTANEOUS VIOLATION OF LORENTZ INVARIANCE AND ULTRA-HIGH ENERGY COSMIC RAYS

2003 ◽  
Vol 12 (07) ◽  
pp. 1279-1287 ◽  
Author(s):  
J. W. MOFFAT
Keyword(s):  
Cosmic Rays ◽  
Lorentz Invariance ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
High Energy ◽  
Spontaneous Breaking ◽  
Ultra High Energy ◽  
High Energy Cosmic Rays ◽  
High Energies ◽  
Local Lorentz Invariance

We propose that local Lorentz invariance is spontaneously violated at high energies, due to a nonvanishing vacuum expectation value of a vector field ϕμ, as a possible explanation of the observation of ultra-high energy cosmic rays with an energy above the GZK cutoff. Certain consequences of spontaneous breaking of Lorentz invariance in cosmology are discussed.

scholarly journals (j, 0) ⊕ (0, j) COVARIANT SPINORS AND CAUSAL PROPAGATORS BASED ON WEINBERG FORMALISM

1993 ◽  
Vol 02 (02) ◽  
pp. 397-422 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
D.J. ERNST
Keyword(s):  
Perturbation Theory ◽  
Wave Equations ◽  
Lorentz Invariance ◽  
Free Particle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Arbitrary Spin ◽  
Definition Of ◽  
The Individual ◽  
Particle Propagator

A pragmatic approach to constructing a covariant phenomenology of the interactions of composite high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin j are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.

scholarly journals Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry

2020 ◽  
Vol 35 (27) ◽  
pp. 2050174
Author(s):  
C. A. Escobar ◽  
R. Potting
Keyword(s):  
Lorentz Invariance ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Lorentz Symmetry ◽  
Spontaneous Breaking ◽  
Effective Hamiltonian ◽  
First Order ◽  
Superluminal Motion ◽  
Field Fluctuations ◽  
Nonlinear Vacuum Electrodynamics

We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebański, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 795
Author(s):  
Vincent Lahoche ◽  
Mohamed Ouerfelli ◽  
Dine Ousmane Samary ◽  
Mohamed Tamaazousti
Keyword(s):  
Principal Component Analysis ◽  
Renormalization Group ◽  
Signal Detection ◽  
Detection Threshold ◽  
Principal Component ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Component Analysis ◽  
Slight Generalization ◽  
Nearly Continuous

The tensorial principal component analysis is a generalization of ordinary principal component analysis focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism, based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

scholarly journals Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 127
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Scalar Field ◽  
Vacuum Polarization ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Approximation ◽  
Dimensional Euclidean Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Adjoint Extension

The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ⟨ϕ2(x)⟩ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor ⟨Tμν(x)⟩ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support.

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

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