Related papers: Group theoretical formulation of free fall and pro…
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and D\"oring, as an alternative mathematical structure within which to formulate physical theories. In particular it has been used to reformulate standard…
We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The…
We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many…
It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein…
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the associated one-parameter groups and their…
We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the…
In this paper we discuss a solution of the free particle Schrodinger equation in which the time and space dependence are not separable. The wavefunction is written as a product of exponential terms, Hermite polynomials and a phase. The…
We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum…
Group field theory posits that spacetime is emergent and is hence defined without any background notion of space or time; dynamical questions are formulated in relational terms, in particular using (scalar) matter degrees of freedom as…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the…
In a previous paper, we proposed an approach for the dynamics of 3D bodies and shells based on the use of affine tensors. This new theoretical frame is very large and the applications are not limited to the mechanics of continua. In the…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
In this paper, we study the emergence of circular formation for agents in cyclic pursuit. Each agent is a unicycle traveling at a fixed common forward speed. We first establish a necessary and sufficient condition for the existence of…