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Jose A. Magpantay

Publications and source records attributed to Jose A. Magpantay.

At least 19 recordsLinked to original sources
arXiv2024

Special Relativistic Liouville Equation Completed

In two previous papers, the author raised the possibility of a special relativistic Liouville equation. The conclusion then was yes, such an equation is possible in 8N phase space if a Lorentz-invariant Universal (LiU) time can be defined for all the degrees of freedom. Without this LiU time, the existence of a special relativistic Liouville equation is empty and may just be a waste of time. In this paper, I propose and argue that the LiU time follows from entropy, which should not be surprising given the second law of thermodynamics and the fact that regardless of how temperature and heat transform under Lorentz transformation, the entropy is invariant. Thus, it is natural to define LiU time from entropy.This now completes the existence of a special relativistic Liouville equation, which will determine the Gibbs distribution, the starting point of classical statistical mechanical description of physical systems. To illustrate the formalism, the partition function for the relativistic ideal gas is derived. The result is much simpler than the Juttner gas result.

cond-mat.stat-mech↗
arXiv2023

A Lindbladian From Feynman-Vernon

The effective dynamics of a system interacting with a bath or environment is presented in two ways, (1) the (LGKS) replacement of the von Neuman equation for the density matrix and (2) the Feynman-Vernon path-integral derivation, by integrating out the bath degree of freedom, to arrive at a system's density matrix. In this paper, I connect the two methods by deriving a Lindbladian in a mechanical example, a point particle interacting with a bath of harmonic oscillators, previously considered by Feynman and Vernon (FV) and expounded on later by Caldeira and Leggett (CL). But the (FV)/(CL) results only in non-Markov effect, memory terms from the bath interaction. To derive a Lindbladian, I changed the interaction term they considered to take into account the point particle interacting with the bath harmonic oscillators to something more realistic. From the resulting path-integral expression of the system's propagator for the density matrix, the Lindbladian and non-Markov terms are read for this simple problem. I also point out the causes of these terms, the Markov Lindbladian from the very local interaction of the point particle with the classical solutions of the harmonic oscillator and the non-Markov term from the global interaction of the point particle with the fluctuation of the classical solutions.

quant-ph↗
arXiv2022

A Special Relativistic Liouville Equation Exists

In a previous paper, the author asked the question "Does a Special Relativistic Liouville Equation Exist?'. In this paper, I give an affirmative answer. In 8N phase space, a Hamiltonian is derived by breaking the reparametrization symmetry of the single, Lorentz invariant, mathematical time introduced, which defines the evolution of all phase space variables.

cond-mat.stat-mech↗
arXiv2022

Does A Special Relativistic Liouville Equation Exist?

The Liouville Equation, the starting point of non-relativistic, non-equilibrium classical statistical mechanics, is problematic in special relativity because of two problems. A relativistic Hamiltonian is claimed not to exist for interacting particles and the problem of what time to use since the particles will all have their own time as part of their space-time coordinate. In this paper, I look at this problem and surprisingly found that there is no special relativistic Liouville equation in 8N phase space, where N is the number of particles, because the canonical Hamiltonian is zero for both non-interacting and interacting particles. This is due to the parametrization symmetry in defining a single time for the Liouville equation evolution, which results in a constraint.This is similar to the fact that in general relativity, diffeomorphism invariance of the theory always give a zero Hamiltonian because of a constraint.

cond-mat.stat-mech↗
arXiv2021

Hydrogen Atom in the Cosmic Microwave Background

The cosmic microwave background covers the entire universe, which suggests the absence of ay closed system, except the universe itself. In this paper, I consider the effect of the cosmic microwave background on the hydrogen atom, which must be very small, otherwise, changes in energy levels would have been measurable. But how small is small? This I compute by considering a system in an environment or bath. I derived the bath's, (in this case the CMB) effect on the hydrogen atom in the Feynman-Vernon approach to an open system. The effect is small and quantified in terms of a correction to the hydrogen atom that breaks time-reversal symmetry, as expected of memory effects. This is significant. There are imperceptible changes in the state of the hydrogen atom, which means that the pervasive CMB must have similar small effects on other atoms, thus breaking time-reversal symmetry in all physical systems.

cond-mat.stat-mech↗
arXiv2020

Lindblad Plus From Feynman-Vernon

I show how the Lindblad Plus equation will follow from the Feynman-Vernon theory. The Plus refers to the inclusion of non-Markov processes in the Lindblad equation resulting in an integro-differential general master equation. The equivalence of this general master equation and not the Lindblad equation alone to the Feynman-Vernon theory should be expected because the sum over histories approach of the FV theory clearly includes non-Markov processes, which Lindblad equation ignores. This should close the seeming gap between these two approaches to quantum open systems.

cond-mat.stat-mech↗
arXiv2019

Spontaneous Symmetry Breaking Breaks Time-Reversal Symmetry

The ideas related to the arrow of time are discussed briefly. I then focus on the prevalent physical mechanism in the evolution of the universe and developments in particle physics, spontaneous symmetry breaking, and show that it explicitly breaks time-reversal symmetry. For simplicity, I do this in a point mechanics gauge theory with symmetry group O(2). The proof of breakdown of time-reversal symmetry relies on the use of a time step function to express the Lagrangian valid for any time.

physics.gen-ph↗
arXiv2019

$ \dfrac{1}{c^2} $ Correction to Thermodynamics

I work out the general expressions for the first relativistic correction of order $ \dfrac{1}{c^2} $ to thermodynamics. The starting point is the relativistic Hamiltonian that I derived in a previous paper, which I expanded to powers of $ \dfrac{1}{c^2} $ to derive a local (in time) Hamiltonian. Limiting to the first relativistic correction, I worked out in general how the relativistic corrections to thermodynamics arise. I then applied the formalism to the problem of N particles with harmonic oscillator interaction in 3D to see the explicit expressions for relativistic corrections.

cond-mat.stat-mech↗
arXiv2018

A Hamiltonian for Relativistic Interacting Many Particles

There is no relativistic Hamiltonian for many particles systems except for free particles and this has been accepted since the 1960s from the work of Currie, Jordan and Sudarshan, Cannon and Jordan, and Leutwyler. This is the problem we will address in this paper by coupling relativistic particles with a scalar field. The Hamiltonian we derive is explicitly relativistic and in the non-relativistic limit gives a Hamiltonian with two body interaction. However, we find that the Poincare algebra is still not satisfied because of the inherent time delayed interaction in relativistic particle systems.

physics.class-ph↗
arXiv2017

Nonlinear Gauge, Stochasticity and Confinement

I clarify, restate and show more clearly some key points I raised in a number of papers that discussed the non-linear gauge-fixing condition and quark confinement. I also correct some errors, which do not detract from the key findings, found in the original papers. However, there are two major corrections I will make in this paper, the first is on the proof of the Parisi-Sourlas mechanism and the second is on the effective action for the 'gluons', which leads to a direct proof of gluons being confined inside hadrons. The correction also leads to how the mass gap will be calculated, which was explicitly done in 2D. The starting point is that contrary to the prevailing ideas in the literature, the Coulomb gauge is an incomplete gauge-fixing condition in the sense that there are field configurations that cannot be gauge transformed to the Coulomb gauge. In other words the orbit of these configurations will not intersect the Coulomb gauge surface. I proposed the non-linear gauge condition precisely because it includes the Coulomb gauge in the high energy (short distance) regime and the quadratic regime (the large distance regime where the running coupling becomes large), where the gauge fields cannot be gauge transformed to the Coulomb surface. We proposed a new decomposition of the gauge potential in the non-linear regime, which involves an isoscalar (the divergence of the gauge field) and a new vector field, which exhibits a mass gap and confinement. When we add the quarks, we find that they are localized to a given distance scale and has an effective four-Fermi action with a linear potential. Thus, we have shown a mass gap for gluons and confinement for both dynamical quarks and gluons.

hep-th↗
arXiv2016

Path Integral Solutions to the Distributions of Statistical Mechanics

We present the path-integral solutions to the distributions in classical (Gibbs) and quantum (Wigner) statistical mechanics. The kernel of the distributions are derived in two ways - one by time slicing and defining the appropriate short-time interval phase space matrix element and second by making use of the kernel in the path-integral approach to quantum mechanics. We show that the two approaches are perturbatively identical. We also present another computation for the Wigner kernel, which is also the Liouville kernel, for the harmonic oscillator and free particle. These kernels may be used as the starting point in the perturbative expansion of the Wigner kernel for any potential. With the kernel solved, we essentially solve also the distributions in classical and quantum statistical mechanics.

cond-mat.stat-mech↗
arXiv2014

Solutions to the Classical Liouville Equation

We present solutions to the classical Liouville equation for ergodic and completely integrable systems - systems that are known to attain equilibrium. Ergodic systems are known to thermal equilibrate with a Maxwell-Boltzmann distribution and we show a simple derivation of this distribution that also leads to a derivation of the distribution at any time t. For illustrative purposes, we apply the method to the problem of a one-dimensional gravitational gas even though its ergodicity is debatable. For completely integrable systems, the Liouville equation in the original phase space is rather involved because of the group structure of the integral invariants, which hints of a gauge symmetry. We use Dirac's constrained formalism to show the change in the Liouville equation, which necessitates the introduction of gauge-fixing conditions. We then show that the solution of the Liouville equation is independent of the choice of gauge, which it must be because physical quantities are derived from the distribution. Instead, we derive the solution to the classical Liouville equation in the phase space where the dynamics involve ignorable coordinates, a technique that is akin to the use of the unitarity gauge in spontaneously broken gauge theories to expose the physical degrees of freedom. It turns out the distribution is time-independent and precisely given by the generalized Gibbs ensemble (GGE), which was solved by Jaynes using the method of constrained optimization. As an example, we apply the method to the problem of two particles in 3D interacting via a central potential.

cond-mat.stat-mech↗
arXiv2012

Microscopic Irreversibility and the H Theorem

Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequences on thermodynamic systems. First, we will argue from from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated from the rest of the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant becomes there is no longer microscopic reversibility. At the classical level of thermodynamics system, we show that the H Theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H Theorem, which still shows entropy monotonically increasing. At the quantum level, we show the the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidts's objection to Boltzmann's ideas.

cond-mat.stat-mech↗
arXiv2011

Geodesics, Mass and the Uncertainty Principle in a Warped de Sitter Space-time

We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the 3-brane, the test particle moves with uniform velocity, giving the appearance that it is not subject to a force. But computing the particle's energy using the energy-momentum tensor yields a time-dependent energy that suggests a time-dependent mass. Thus, the extra force, which is the effect of the warped extra dimension on the particle's motion on the 3-brane, does not change the velocity but the mass of the particle. The particle's motion in the bulk also results in a time-dependent modification of the Heisenberg uncertainty principle as viewed on the 3-brane. These two results show that the classical physics along the extra dimension results in the time-dependence of particle masses and the uncertainty principle. If the particle masses are time-independent and the Heisenberg's uncertainty principle is to remain unchanged, then there must be a non-gravitational force that will restrict all particles on the 3-brane. Finally, we just note that although classically, these time-dependent corrections on the 3-brane can be removed, quantum mechanical corrections along the extra dimension will restore back the problem.

gr-qc↗
arXiv2011

Dual DSR

We develop the physics of dual kappa Poincare algebra, which we will call dual DSR. First, we show that the dual kappa Poincare algebra is isomorphic to de Sitter algebra and its spactime is essentially de Sitter spacetime. Second, we show how to derive the coproduct rules for Beltrami and conformal coordinates of de Sitter spacetime. It follows from the current literature on de Sitter relativity that the speed of light c and the de Sitter length are the two invariant scales of the physics of dual kappa Poincare algebra. Third, we derive the Casimir invariant of the dual kappa Popincare algebra and use this to derive an expression for the speed of light, our fourth result. Fifth, the field equation for the scalar field is derived from the Casimir invariant. The results for the coordinate speed of light and the scalar field theory are the same as in de Sitter theory in the planar coordinate basis. Thus, we have shown that the physics of dual kappa Poincare algebra (in the dual bicrossproduct basis), which can be apprpriately called dual DSR, is essentially de Sitter relativity. Sixth, we argue the existence of an observer-independent minimum momentum. Seventh, we argue heuristically that the existence of minimum momentum will lead to a dual generalized uncertainty principle. Finally, we note that dual DSR is not a quantum theory of spacetime but a quantum theory of momenta.

hep-th↗
arXiv2010

Dual Kappa Poincare Algebra

We show a different modification of Poincare algebra that also preserves Lorentz algebra. The change begins with how boosts affect spacetime in a way similar to how they affect the momenta in kappa Poincare algebra, hence the term "dual kappa Poincare algebra". Since by construction the new spacetime commutes, it follows that the momenta co-commute. Proposing a spacetime co-algebra that is similar to the coproduct in the bicrossproduct basis of kappa Poincare algebra, we derive the phase space algebra using the Heisenberg double construction. The phase space variables of the dual kappa Poincare algebra are then related to the SR phase space variables. From these relations, we complete the dual kappa Poincare algebra by deriving the action of rotations and boosts on the momenta.

math-ph↗
arXiv2004

Effective Quantum Dynamics of Quarks and Gluons in a Stochastic Background

The quantum dynamics of quarks, gluons and the scalar degrees of freedom associated with the non-linear regime of the non-linear gauge is derived. We discuss the subtleties in quantizing in a stochastic background. Then we show in detail that the stochastic average of the Yang-Mills action is only dependent on the gluon and not on the scalars thus proving that the scalars are non-propagating. Integrating out the scalars from the stochastically averaged fermion action leads to fermions that decline exponentially. Finally, we derive the effective action of the gluons and fermions resulting from stochastic averaging. We show that it leads to a confining four-fermi interaction.

hep-th↗