Related papers: Quantum mechanical path integrals in the first qua…
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been…
The worldline path integral approach to the Bern-Kosower formalism is reviewed, which offers an alternative to Feynman diagram calculations in quantum field theory. Recent progress in constructing a multiloop generalization of this…
We report on the status of the string-inspired world line path integral formalism, a recently developed powerful tool for the reorganisation of standard perturbative amplitudes in quantum field theory. The method is outlined and the present…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
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…
The worldline formalism provides an alternative to Feynman diagrams that has been found particularly useful for external-field calculations in quantum electrodynamics. Here I summarize its present range of applications, which includes…
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it…
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A…
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
We developed a path integral formalism for the quantum mechanics in a rotating reference of frame, and proposed a spin path integral description for the spin degrees of freedom in it. We have also give some examples for the applications of…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in…