Related papers: Geometrical formulation of quantum fields
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
States in quantum field theory (QFT) are represented by many-particle wave functions, such that a state describing n particles depends on n spacetime positions. Since a general state is a superposition of states with different numbers of…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
For description of the quantum dynamics on a curved group manifold the path integrals in a space of the group parameters is offered. The formalism is illustrated by the $H$-atom problem.
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for…