Related papers: Euclideanization without Complexification of the S…
Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…
By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…
We discuss Wick rotations in the context of gravity, with emphasis on a non-perturbative Wick rotation proposed in hep-th/0103186 mapping real Lorentzian metrics to real Euclidean metrics in proper-time coordinates. As an application, we…
The starting point of this work is the principle that all movement of particles and photons must follow geodesics of a 4-dimensional space where time intervals are always a measure on geodesic arc lengths. The last 3 coordinates (alpha =…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
We review the algebraic field theory based completely on a nonlinear generalization of the CR complex analiticity conditions to the noncommutative algebra of biquaternions. Any biquaternionic field possesses natural twistor structure and,…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
We consider a two-time (characterized by distinct speeds of causality) and three-space-dimensional Minkowski space and derive relativistic coordinate and velocity transformation formulas and expressions for a new effective speed limit.…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
Conics in the Euclidean space have been known for their geometrical beauty and also for their power to model several phenomena in real life. It usually happens that when thinking about the conics in a semi-Riemannian manifold, the equations…
Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds…
Four-dimensional Euclidean spaces that solve Einstein's equations are interpreted as WKB approximations to wavefunctionals of quantum geometry. These spaces are represented graphically by suppressing inessential dimensions and drawing the…
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise…
The aim of this paper is to find out a correspondence between one-loop effective action $W_E$ defined by means of path integral in Euclidean gravity and the free energy $F$ obtained by summation over the modes. The analysis is given for…
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead…