arXiv subjects

M. C. Rocca

Publications and source records attributed to M. C. Rocca.

At least 19 recordsLinked to original sources

arXiv2021

Gupta-Feynman based Quantum Field Theory of Einstein's Gravity

This paper is an {\sf application} to Einstein's gravity (EG) of the mathematics developed in A. Plastino, M. C. Rocca: J. Phys. Commun. {\bf 2}, 115029 (2018). We will quantize EG by appeal to the most general quantization approach, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the functional integral method, when we are in the presence of derivative couplings \nd We base our efforts on works by Suraj N. Gupta and Richard P. Feynman so as to undertake the construction of a Quantum Field Theory (QFT) of Einstein Gravity (EG). We explicitly use the Einstein Lagrangian elaborated by Gupta \cite{g1} but choose a new constraint for the theory that differs from Gupta's one. In this way, we avoid the problem of lack of unitarity for the $S$ matrix that afflicts the procedures of Gupta and Feynman. Simultaneously, we significantly simplify the handling of constraints. This eliminates the need to appeal to ghosts for guarantying the unitarity of the theory. Our ensuing approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing tho the mathematical theory developed by Bollini et al. \cite{tp3,tp18,tp19,tp20,pr} Such developments were founded in the works of Alexander Grothendieck \cite{gro} and in the theory of Ultradistributions of Jose Sebastiao e Silva \cite{tp6} (also known as Ultrahyperfunctions). Based on these works, we have constructed a mathematical edifice, in a lapse of about 25 years, that is able to quantize non-renormalizable Field Theories (FT). Here we specialize this mathematical theory to treat the quantum field theory of Einsteins's gravity (EG). Because we are using a Gupta-Feynman inspired EG Lagrangian, we are able to evade the intricacies of Yang-Mills theories.

physics.gen-ph↗

arXiv2021

Coherent and cat states of open and closed strings

The covariant quantization and light cone quantization formalisms are followed to construct the coherent states of both open and closed bosonic strings. We make a systematic and straightforward use of the original definition of coherent states of harmonic oscillators to establish the coherent and their corresponding cat states. We analyze the statistics of these states by explicitly calculating the Mandel parameter and obtained interesting results about the nature of distribution of the states. A tachyonic state with imaginary mass and the positive norm is obtained.

hep-th↗

arXiv2021

Supercoherent states of the open NS world sheet superstring

The supercoherent states of the RNS string are constructed using the covariant quantization and analogously the light cone quantization formalisms. Keeping intact the original definition of coherent states of harmonic oscillators, we extend the bosonic annihalation operator into the superspace by inclusion of fermionic contribution to oscillator modes thus construct the supercoherent states with supersymetric harmonic oscillator. We analyse the statistics of these states by explicitly calculating the Mandel parameter and obtained interesting results about the nature of distribution of the states

hep-th↗

arXiv2021

Gravitational partition function modified by super-light brane world perturbative modes

In this paper, we will analyze the effects of super-light brane world perturbative modes on clustering of galaxies. In present manuscript, we use the Boltzmann and Tsallis statistical approaches to study the large distance modification of gravity in the brane world. The impact of modified potential on clustering of galaxies is analyzed in both the approaches. The infinities associated with Newtonian point mass approximation of gravity models is removed using the analytical extensions. The regularized and finite partition function is obtained for the system of galaxies in the brane world model and is used to evaluate the regularized thermodynamic properties of the system in the form of equations of state. Hence, we study thermodynamic quantities and discuss about the thermodynamic stability of the model. We find that large number of galaxies may lead to the thermodynamic instability.

hep-th↗

arXiv2021

Two approaches that prove divergence free nature of non-local gravity

This paper is an attempt to study the thermodynamics of the structure formation in the large scale universe in the non local gravity using Boltzmann statistics and the Tsallis statistics. The partition function is obtained in both the approaches and the corresponding thermodynamics properties are evaluated. The important thing about the paper is that we surprisingly get the divergence free integrals and thus stress upon the fact that the nonlocal gravity is the singularity free model of gravity.

gr-qc↗

arXiv2020

Boltzmann and Tsallis statistical approaches to study Quantum corrections at large distances and clustering of galaxies

Gravity is so different from other fundamental forces that it is now essentially treated as a non-fundamental force of entropic origin. A number of good studies have been carried out in this direction. Quantum gravity has also significantly improved our understanding by combining gravity well with quantum physics. However, there are still many impediments to our understanding especially in the limits of extreme. The effects of quantum gravity start appearing on the scene at Planck length which is the smallest length in nature idealized so far. While as this study incorporates a model which is valid for potential energy corrections at small distances but we have also given a bold try to use it confidently for the corrections at very large distances as well. The model uses two techniques namely Boltzmann and Tsallis statistical approaches to explore the thermodynamics within the ambit of brane world model giving its further modified version. We have computed partition function by using both Boltzmann and Tsallis statistical approaches and then used it to study thermodynamics of the brane world model. We have analyzed both analytically and graphically, the thermodynamic quantities like Helmholtz free energy and specific heat. The thermodynamic stability of the model is also discussed depending on the number of galaxies.

gr-qc↗

arXiv2019

Relativistic treatment of Verlinde's emergent force in Tsallis' statistics

Following Chakrabarti,Chandrasekhar, and Naina [Physica A {\bf 389} (2010) 1571], we attempt a classical relativistic treatment of Verlinde's emergent entropic force conjecture by appealing to a relativistic Hamiltonian in the context of Tsalli's statistics. The ensuing partition function becomes the classical one for small velocities. We show that Tsallis' relativistic (classical) free particle distribution at temperature $T$ can generate Newton's gravitational force's $r^{-2}$ {\it distance's dependence}. If we want to repeat the concomitant argument by appealing to Renyi's distribution, the attempt fails and one needs to modify the conjecture.

cond-mat.stat-mech↗

arXiv2019

An Entropic Force Schrödringer mechanism for Dark Matter generation

Theorists of entropic (emergent) gravity put forward that what has been regarded as unobserved dark matter might instead be the product of quantum effects that can be looked at as emergent energy (EE). Here we describe a novel Schrödringer mechanism (SM). This SM uncovers the existence of new quantum gravitational states that could be associated to the above mentioned EE. This is done on the basis of the microscopic Verlinde-like entropic force advanced in [Physica A {\bf 511} (2018) 139], that deviates from the Newton's form at extremely short distances.

physics.gen-ph↗

arXiv2019

A rigorous calculation of the Feynman and Wheeler Scalar Fields propagators in the ADS / CFT correspondence using distribution theory

By appeal to Distribution Theory we discuss in rigorous fashion, without appealing to {\bf any conjecture} (as usually done by other authors), the boundary-bulk propagators for the scalar field, both in the non-massive and massive cases. These calculations, new in the literature as far as we know, are carried out in two instances: (i) when the boundary is a Euclidean space and (ii) when it is of Minkowskian nature. In this last case we compute also three propagators: Feynman's, Anti-Feynman's, and Wheeler's (half advanced plus half retarded). For an operator corresponding to scalar field we obtain the two points correlations functions in the three instances above mentioned

hep-th↗

arXiv2018

Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture

Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in [Physica A {\bf 505} (2018) 190] within a purely classical statistical context, and in [DOI: 10.13140/RG.2.2.34454.24640] for the case of bosons' statistics. In the present work, we appeal to a quantum scenario involving fermions' statistics. We consider also the classical limit of quantum (statistical) mechanics (QM). We encounter a lower bound to the distance $r$ between the two interacting masses, i.e., an $r$ cut-off. This is a new effect that exhibits some resemblance with the idea of space discretization proposed by recent gravitation theories

physics.gen-ph↗

arXiv2018

Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions

The Dimensional Regularization of Bollini and Giambiags (Phys. Lett. {\bf B 40}, 566 (1972), Il Nuovo Cim. {\bf B 12}, 20 (1972). Phys. Rev. {\bf D 53}, 5761 (1996)) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) ${\cal S}^{'}_L$. In this paper we overcome here such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained in [Int. J. of Theor. Phys. {\bf 43}, 1019 (2004)] and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J. Sebastiao e Silva [Math. Ann. {\bf 136}, 38 (1958)], also known as Ultrahyperfunctions, obtained by Bollini et al. [Int. J. of Theor. Phys. {\bf 38}, 2315 (1999), {\bf 43}, 1019 (2004), {\bf 43}, 59 (2004),{\bf 46}, 3030 (2007)]. Using the Inverse Fourier Transform we get the ring with zero divisors ${\cal S}^{'}_{LA}$, defined as ${\cal S}^{'}_{LA}={\cal F}^{-1}\{{\cal S}^{'}_L\}$, where ${\cal F}^{-1}$ denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring ${\cal S}^{'}_{L}$) via convolution, and a product of distributions in the corresponding configuration space (the ring ${\cal S}^{'}_{LA})$. This generalizes the results obtained by Bollini and Giambiagi for Euclidean space in [Phys. Rev. {\bf D 53}, 5761 (1996)]. We provide several examples of the application of our new results in Quantum Field Theory. In particular, the convolution of $n$ massless Feynman propagators and the convolution of n massless Wheeler propagators in Minkowskian space.

physics.gen-ph↗

arXiv2018

Quantum statistical treatment of Verlinde's conjecture in a Tsallis framework

Verlinde has recently conjectured, via a Beckenstein-like thought experiment, that gravitation, instead of being an elementary force, is an emergent entropic one. This rather surprising conjecture was actually proved in [Physica A {\bf 505} (2018) 190], in a strictly classical statistical mechanics' environment. In this Communication, we work in a quantum statistical context to consider the conjecture in the case of bosons/fermions, in a Tsallis' framework. We prove that Tsallis' entropy is the operating potential energy in this quantum treatment, something that does not happen in the case of Boltzmann-Gibbs' entropy. \color{red} In the classical limit, we show that the emergent force has a Newtonian dependence with the distance.

physics.gen-ph↗

arXiv2018

Reciprocity relations and generalized entropic quantifiers that lack trace-form

In this effort we show that the Legendre reciprocity relations,thermodynamic's essential formal feature, are respected by any entropic functional, even if it is NOT of trace-form nature, as Shannon's is. Further, with reference to the MaXent variational process, we encounter important cases, relevant to physical applications currently discussed in the research literature, in which the associated reciprocity relations exhibit anomalies. We show that these anomalies can be cured by carefully discriminating between apparently equivalent entropic forms.

cond-mat.stat-mech↗

arXiv2018

Features of constrained entropic functional variational problems

We describe in great generality features concerning constrained entropic, functional variational problems that allow for a broad range of applications. Our discussion encompasses not only entropies but, potentially, any functional of the probability distribution, like Fisher-information or relative entropies, etc. In particular, in dealing with generalized statistics in straightforward fashion one may sometimes find that the first thermal law $\frac{dS}{dβ}=β\frac{d }{dβ}$ seems to be not respected. We show here that, on the contrary, it is indeed obeyed by any system subject to a Legendre extremization process, i.e., in all constrained entropic variational problems.

cond-mat.stat-mech↗

arXiv2018

Quantum treatment of Verlinde's entropic force conjecture

Verlinde conjectured that gravitation is an emergent entropic force. This surprising conjecture was proved in [Physica A {\bf 505} (2018) 190] within a purely classical context. Here, we appeal to a quantum environment to deal with the conjecture in the case of bosons and consider also the classical limit of quantum mechanics (QM).

physics.gen-ph↗

arXiv2018

Verlinde's emergent gravity in an $\boldsymbol{n-}$dimensional, non-additive Tsallis' scenario

This paper brings together four distinct but very important physical notions: 1) Entropic force, 2) Entropy-along-a-curve, 3) Tsallis' q-statistics, and 4) Emergent gravitation. We investigate the non additive, classical (Tsallis') q-statistical mechanics of a phase-space curve in $n$ dimensions (3 dimensions, in particular). We focus attention on an entropic force mechanism that yields a simple realization of it, being able to mimic interesting effects such as confinement, hard core, and asymptotic freedom, typical of high energy physics

physics.gen-ph↗

arXiv2018

Newton's gravitation-force's classical average proof of a Verlinde's conjecture

A surprising, gravity related Verlinde-conjecture, that generated immense interest, asserts that gravity is an emergent entropic force. We provided a classical proof of the assertion in [doi.org/j.physa.2018.03.019]. Here, we classically prove a related, second Verlinde-conjecture. This states that, at very large distances ($r_0$), gravity departs from its classical nature and begins to decay linearly with $r_0$.

physics.gen-ph↗

arXiv2018

Tsallis' Quantum q-Fields

We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated to them in recent literature. We refer to the q-Schrödinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, [Phys. Rev. Lett. {\bf 106}, 140601 (2011), EPL {\bf 118}, 61004 (2017) and references therein]. Also, we introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and not-Abelian instances. We show how to define the q-Quantum Field Theories corresponding to the above equations, introduce the pertinent actions, and obtain motion equations via the minimum action principle. These q-fields are meaningful at very high energies (TeVs) for $q=1.15$, high ones (GeVs) for $q=1.001$, and low energies (MeVs)for $q=1.000001$ [Nucl. Phys. A {\bf 955} (2016) 16 and references therein]. (See the Alice experiment of LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.

physics.gen-ph↗