Related papers: On the quantization of nonlocal theory
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…
In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical…
We consider recently developed Cohomological Field Theory soliton counting diagram technique for Khovanov and Khovanov-Rozansky invariants [1,2]. Although the expectation to obtain a new way for computing the invariants has not yet come…
We develop a quantitative theory of stochastic homogenization in the more general framework of differential forms. Inspired by recent progress in the uniformly elliptic setting, the analysis relies on the study of certain subadditive…
We discuss the locality problem in relativistic and nonrelativistic quantum theory. We show that there exists a formulation of quantum theory that, on one hand, preserves the mathematical apparatus of the standard quantum mechanics and, on…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
The basic physical structure of the relativistic theory of gravitation is discussed. The significant role that the Hypothesis of Locality plays in relativity theory is elucidated via the phenomenon of spin-rotation coupling. The limitations…
String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as $e^{\ell^2 \Box / 2}$ in the vertices. This nonlocality has hindered the…
A critique of the state of current quantum theory in physics is presented, based on a perspective outside the normal physics training. From this perspective, the acceptance of quantum nonlocality seems unwarranted, and the fundamental…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a four-dimensional 'space-time' by an action resembling closely the self-dual Plebanski…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
Based on our model of quantum systems as emerging from the coupled dynamics between oscillating "bouncers" and the space-filling zero-point field, a sub-quantum account of nonlocal correlations is given. This is explicitly done for the…
Tomographic locality is a principle commonly used in the program of finding axioms that pick out quantum theory within the landscape of possible theories. The principle asserts the sufficiency of local measurements for achieving a…
The theory of relativistic strings is considered in frames of Hamiltonian formalism and Dirac's quantization procedure. A special gauge fixing condition is formulated, related with the world sheet of the string in Lorentz-invariant way. As…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…