相关论文: On the formulations of the Fermat principle in gen…
It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point (emission event) to a timelike curve (worldline of…
In this paper we use a general version of Fermat's principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian…
Fermat's principle is fully generalized to the case where a smooth interface separates two cone structures -- Lorentz-Finsler lightcones -- representing wave propagation in a potentially inhomogeneous, anisotropic, time-dependent and…
The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which…
New form of Fermat's principle for light propagation in arbitrary (i.e. in general neither static nor stationary) gravitational field is proposed. It is based on Herglotz extension of canonical formalism and simple relation between the…
We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a…
We apply Perlick's (1990a) rigorous formulation of the Fermat principle in arbitrary spacetimes to prove the correctness of the description of gravitational lensing by gravitational waves, given in the literature using the scalar and vector…
We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…
In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…
Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the…
Fermat's principle and variational analysis is used to analyze the trajectories of light propagating in a radially inhomogeneous medium with a singularity in the center. It is found that the light trajectories are similar to those around a…
We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian space-time, tetrads, connection one-forms,…