scholarly journals The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
D. Dudal ◽  
G. Peruzzo ◽  
S. P. Sorella
Keyword(s):  
Vector Boson ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Equivalence Theorem ◽  
Higgs Model ◽  
Stationary Condition ◽  
Ward Identities ◽  
Complex Scalar ◽  
Current Case ◽  
Gauge Invariant

Abstract The content of two additional Ward identities exhibited by the U(1) Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs particle and the massive vector boson is introduced in the theory from the beginning. Among the results obtained from the above mentioned Ward identities, we underline a new exact relationship between the stationary condition for the vacuum energy, the vanishing of the tadpoles and the vacuum expectation value of the gauge invariant scalar operator. We also present a characterization of the two-point correlation function of the composite operator corresponding to the vector boson in terms of the two-point function of the elementary gauge fields. Finally, a discussion on the connection between the cartesian and the polar parametrization of the complex scalar field is presented in the light of the Equivalence Theorem. The latter can in the current case be understood in the language of a constrained cohomology, which also allows to rewrite the action in terms of the aforementioned gauge invariant operators. We also comment on the diminished role of the global U(1) symmetry and its breaking.

scholarly journals NONPERTURBATIVE FIELD CORRELATOR AND STRING REPRESENTATION FOR THE 't HOOFT LOOP AVERAGE IN THE ABELIAN HIGGS MODEL

1998 ◽  
Vol 13 (09) ◽  
pp. 659-671 ◽  
Author(s):  
D. V. ANTONOV
Keyword(s):  
Field Strength ◽  
Higgs Field ◽  
Exact Result ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
String Tension ◽  
Higgs Model ◽  
Effective Theory ◽  
Abelian Higgs Model ◽  
String Representation

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs model string representation for the 't Hooft loop average defined on the string worldsheet, which yields the values of two coefficient functions parametrizing the bilocal correlator of the dual field strength tensors. The asymptotic behaviors of these functions agree with the ones obtained within the method of vacuum correlators in QCD in the lowest order of perturbation theory. We demonstrate that the bilocal approximation to the method of vacuum correlators is an exact result in the Londons' limit, i.e. all the higher cumulants in this limit vanish. We also show that at large distances, apart from the integration over metrics, the obtained string effective theory (which in this case reduces to the nonlinear massive axionic sigma model) coincides with the low energy limit of the dual version of 4D compact QED, the so-called universal confining string theory. We derive string tension of the Nambu–Goto term and the coupling constant of the rigidity term for the obtained string effective theory and demonstrate that the latter is always negative, which means the stability of strings, while the positiveness of the former is confirmed by the present lattice data. These data enable us to find the Higgs boson charge and the vacuum expectation value of the Higgs field, which well-described QCD. We also study dynamics of the weight factor of the obtained string representation for the 't Hooft average in the loop space. In conclusion, we obtain string representation for the partition function of the correlators of an arbitrary number of Higgs currents, by virtue of which we rederive the structure of the bilocal correlator of the dual field strength tensors, which yields the surface term in the string effective action.

scholarly journals Lorentz-Violating Gravity Models and the Linearized Limit

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 490 ◽  
Author(s):  
Michael Seifert
Keyword(s):  
Differential Forms ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Gravity Models ◽  
Effective Equation ◽  
Gauge Invariant ◽  
Coupled Equations ◽  
Klein Gordon ◽  
Local Geometric Structure ◽  
Do So

Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects.

scholarly journals WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES

2000 ◽  
Vol 15 (08) ◽  
pp. 541-546 ◽  
Author(s):  
SATISH. D. JOGLEKAR ◽  
A. MISRA
Keyword(s):  
Finite Field ◽  
Wilson Loop ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Gauge Invariant ◽  
Expectation Value ◽  
Direct Verification ◽  
Axial Gauge ◽  
Field Dependent ◽  
New Treatment

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that under the FFBRS transformation as the vacuum expectation value of a gauge-invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Furthermore, we give an argument for direct verification of the invariance of Wilson loop to O(g4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g2).

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

scholarly journals Minimal scoto-seesaw mechanism with spontaneous CP violation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
D. M. Barreiros ◽  
F. R. Joaquim ◽  
R. Srivastava ◽  
J. W. F. Valle
Keyword(s):  
Dark Matter ◽  
Cp Violation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Discrete Symmetry ◽  
Double Beta Decay ◽  
Neutrino Masses ◽  
Seesaw Mechanism ◽  
Cosmological Observations ◽  
Scalar Singlet

Abstract We propose simple scoto-seesaw models to account for dark matter and neutrino masses with spontaneous CP violation. This is achieved with a single horizontal $$ {\mathcal{Z}}_8 $$ Z 8 discrete symmetry, broken to a residual $$ {\mathcal{Z}}_2 $$ Z 2 subgroup responsible for stabilizing dark matter. CP is broken spontaneously via the complex vacuum expectation value of a scalar singlet, inducing leptonic CP-violating effects. We find that the imposed $$ {\mathcal{Z}}_8 $$ Z 8 symmetry pushes the values of the Dirac CP phase and the lightest neutrino mass to ranges already probed by ongoing experiments, so that normal-ordered neutrino masses can be cornered by cosmological observations and neutrinoless double beta decay experiments.

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