Related papers: On Dirac's Delta Calculus
We present an analytical framework for studying quantum tunneling through multiple Dirac delta potential barriers in one dimension. Using the transfer matrix method, we derive a closed-form expression for the total transfer matrix of a…
We discuss a generalized representation of the Dirac delta function in $d$ dimensions in terms of $q$-exponential functions. We apply this new representation to the study of the so-called $q$-Fourier transform, proving its invertibility for…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are…
Czachor's recent proposal introduces a form of non-Newtonian calculus built by pulling back arithmetic operations through arbitrary bijections between continua. Although the idea is mathematically inventive, it runs into serious conceptual…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…
Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…
The interpretation of an experimental realization of Wheeler's delayed-choice gedanken experiment is discussed and called into question.
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…
Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical…
In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes for a type of generalized cubic theta functions.
This paper examines the Foldy-Wouthuysen and Feynman-Gell-Mann representations of the Dirac equation. The analysis is conducted for electrons and positrons interacting with electromagnetic fields. Versions of quantum electrodynamics are…
Within the overlap framework, I derive the main formulae one finds today in papers touting a ``new approach'' to the regularization of chiral gauge theories. My main objective is to clear up an unhealthy confusion about how many successful…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the…
In J.D. Jackson's Classical Electrodynamics textbook, the analysis of Dirac's charge quantization condition in the presence of a magnetic monopole has a mathematical omission and an all too brief physical argument that might mislead some…