scholarly journals Can quantum fluctuations differentiate between standard and unimodular gravity?

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Gustavo P. de Brito ◽  
Oleg Melichev ◽  
Roberto Percacci ◽  
Antonio D. Pereira
Keyword(s):  
Scalar Field ◽  
Path Integral ◽  
Invariant Theory ◽  
Quantum Fluctuations ◽  
Quantization Procedure ◽  
Gauge Fixing ◽  
Theory Of Gravity ◽  
Definition Of

Abstract We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.

scholarly journals Physical quantities and arbitrariness in resolving quantum master equation

2017 ◽  
Vol 32 (11) ◽  
pp. 1750068 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov
Keyword(s):  
Master Equation ◽  
Path Integral ◽  
Quantum Master Equation ◽  
Abelian Gauge ◽  
Quantization Procedure ◽  
Gauge Fixing ◽  
Physical Quantities

By proceeding with the idea that the presence of physical (BRST invariant) extra factors in the path integral is equivalent to taking into account explicitly the arbitrariness in resolving the quantum master equation, we consider the field–antifield quantization procedure both with the Abelian and the non-Abelian gauge fixing.

scholarly journals SMOOTHED QUANTUM FLUCTUATIONS AND CMB OBSERVATIONS

2012 ◽  
Vol 21 (10) ◽  
pp. 1250080
Author(s):  
JAKUB MIELCZAREK ◽  
MICHAŁ KAMIONKA
Keyword(s):  
Scalar Field ◽  
Power Spectrum ◽  
Internal Structure ◽  
Planck Scale ◽  
Quantum Fluctuations ◽  
Gaussian Smoothing ◽  
Cosmic Inflation ◽  
Smoothing Factor ◽  
High Multipoles

In this paper, we investigate power spectrum of a smoothed scalar field. The smoothing leads to regularization of the UV divergences and can be related with the internal structure of the considered field or the space itself. We perform Gaussian smoothing to the quantum fluctuations generated during the phase of cosmic inflation. We study whether this effect can be probed observationally and conclude that the modifications of the power spectrum due to the smoothing on the Planck scale are negligible and far beyond the observational abilities. Subsequently, we investigate whether smoothing in any other form can be probed observationally. We introduce phenomenological smoothing factor e-k2σ2 to the inflationary spectrum and investigate its effects on the spectrum of CMB anisotropies and polarization. We show that smoothing can lead to suppression of high multipoles in the spectrum of the CMB. Based on seven years observations of WMAP satellite we indicate that the present scale of high multipoles suppression is constrained by σ < 3.19 Mpc (95% CL). This corresponds to the constraint σ < 100 μm at the end of inflation. Despite this value is far above the Planck scale, other processes of smoothing can be possibly studied with this constraint, as decoherence or diffusion of primordial perturbations.

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

2012 ◽  
Vol 27 (27) ◽  
pp. 1250157 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Mass Term ◽  
Light Front ◽  
Light Cone Gauge ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
New Class ◽  
Gauge Fixing ◽  
Form Theory

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

GALACTIC AND ASTROPHYSICAL SIZES FROM SCALAR-TENSOR THEORY OF GRAVITY

2004 ◽  
Vol 13 (02) ◽  
pp. 359-371 ◽  
Author(s):  
GIUSEPPE BASINI ◽  
MARCO RICCI ◽  
FULVIO BONGIORNO ◽  
SALVATORE CAPOZZIELLO
Keyword(s):  
Scalar Field ◽  
Spiral Galaxies ◽  
Weak Field ◽  
Newtonian Potential ◽  
Scalar Tensor Theory ◽  
Field Limit ◽  
Weak Field Limit ◽  
Tensor Theory ◽  
Flat Rotation Curves ◽  
Theory Of Gravity

We investigate the weak-field limit of scalar-tensor theory of gravity and show that results are directly depending on the coupling and self-interaction potential of the scalar field. In particular, corrections are derived for the Newtonian potential. We discuss astrophysical applications of the results, in particular the flat rotation curves of spiral galaxies.

scholarly journals ON THE QUANTUM CHROMODYNAMICS OF A MASSIVE VECTOR FIELD IN THE ADJOINT REPRESENTATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350054 ◽  
Author(s):  
ALFONSO R. ZERWEKH
Keyword(s):  
Vector Field ◽  
Quantum Chromodynamics ◽  
Extra Dimensions ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Adjoint Representation ◽  
Coupling Constants ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Definition Of

In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that gauge invariance is not enough to constraint the couplings. Nevertheless, the requirement of unitarity fixes the values of the coupling constants, which otherwise would be arbitrary. Additionally, it opens a new discrete symmetry which makes the coloron stable and avoid its resonant production at a collider. On the other hand, a judicious definition of the gauge fixing terms modifies the propagator of the massive field making it well-behaved in the ultraviolet limit. The relation between our model and the more general approach based on extended gauge symmetries is also discussed.

scholarly journals ABELIAN ANOMALIES IN NONLOCAL REGULARIZATION

1994 ◽  
Vol 09 (26) ◽  
pp. 4549-4564 ◽  
Author(s):  
M.A. CLAYTON ◽  
L. DEMOPOULOS ◽  
J.W. MOFFAT
Keyword(s):  
Path Integral ◽  
Invariant Theory ◽  
Axial Anomaly ◽  
Regularization Scheme ◽  
Integral Measure ◽  
Nonlocal Regularization ◽  
Noether Current

The nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the merits and new features of the regularization scheme, as well as the barrier to quantizing the fully gauged chiral-invariant theory.

scholarly journals Inflation constraints for classes of f(R) models

2018 ◽  
Vol 15 (12) ◽  
pp. 1850209
Author(s):  
Joseph Ntahompagaze ◽  
Jean Damascène Mbarubucyeye ◽  
Shambel Sahlu ◽  
Amare Abebe
Keyword(s):  
Scalar Field ◽  
Early Universe ◽  
First Derivative ◽  
A Value ◽  
Slow Roll ◽  
Theories Of Gravity ◽  
Text Model ◽  
Definition Of ◽  
Inflationary Parameters

In this paper, we explore the equivalence between two theories, namely [Formula: see text] and scalar–tensor theories of gravity. We use this equivalence to explore several [Formula: see text] toy models focusing on the inflation epoch of the early universe. The study is done based on the definition of the scalar field in terms of the first derivative of [Formula: see text] model. We have applied the slow-roll approximations during inflationary parameters consideration. The comparison of the numerically computed inflationary parameters with the observations is done. We have inspected that some of the [Formula: see text] models produce numerical values of [Formula: see text] that are in the same range as the suggested values from observations. But for the case of the tensor-to-scalar ratio [Formula: see text], we realized that some of the considered [Formula: see text] models suffer to produce a value which is in agreement with the observed values for different considered space parameter.

scholarly journals COORDINATE-INVARIANT PATH INTEGRAL METHODS IN CONFORMAL FIELD THEORY

2006 ◽  
Vol 21 (17) ◽  
pp. 3525-3563 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Direct Calculation ◽  
Conformal Anomaly ◽  
Operator Formalism ◽  
Conformal Field ◽  
Integral Methods ◽  
Change Of Variables ◽  
Definition Of

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

PATH INTEGRAL CALCULATION OF GREEN’S FUNCTION FOR SCHRÖDINGER EQUATION IN UNITARY GAUGE

1992 ◽  
Vol 07 (31) ◽  
pp. 7775-7786
Author(s):  
L. ROZANSKY
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Preexponential Factor ◽  
Unitary Gauge ◽  
Gauge Fixing

Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.

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