Related papers: The Generalized Gell-Mann--Low Theorem for Relativ…
For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem…
We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…
We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her…
We discuss a free scalar field subject to generalized Wentzell boundary conditions. On the classical level, we prove well-posedness of the Cauchy problem and in particular causality. Upon quantization, we obtain a field that may naturally…
We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons.…
Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…
Algebraic non-covariant gauges are used often in string theory, Chern-Simons theory, gravitation and gauge theories. Loop integrals, however, have spurious singularities that need to be regularized. The most popular and consistent…
A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described…
The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic…
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a…
The so called Gell-Mann or decontraction formula is proposed as an algebraic expression inverse to the Inonu-Wigner Lie algebra contraction. It is tailored to express the Lie algebra elements in terms of the corresponding contracted ones.…
In this paper, we explore the Klein-Gordon field theory in $(D+1)$ dimensions in the presence of a $(D-1)$-dimensional hyperplanar $\delta$-like potential that couples quadratically to the field derivatives. This model effectively…
The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…