Related papers: Physics of Finance
We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it "Field's dilemma", referring…
We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our…
Quantization of field theories with gauge symmetry is an extensively discussed and well-established topic. In this short note, we revisit this old problem. While we confirm all details of the existing literature, we highlight a potentially…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given. Because the constraints are compatible with the field equations they remain so. We study a model…
The construction of a gauge field theory for elementary particles usually starts by promoting global invariance of the matter action to a local one, this in turn implying the introduction of gauge fields. We present here a procedure that…
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
Perhaps the most important contribution of gauge theory to general mathematics is to point out the importance of association functors. Emphasizing category theory we characterize association functors by two of their natural properties and…
Linear lattice gauge theory is based on link variables that are arbitrary complex or real $N\times N$ matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space…
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
This series of lectures is planned as a generalization of author's large (more than fifteen years) experience of work in the theoretical physics. The modern theoretical physics is based on the group-theoretical approach which generates the…
If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this…
In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current,…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…
Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In this paper, by comparing the geometric structure of…
We develop a theory of securities price formation and dynamics based on quantum approach and without presuming any similarities with quantum mechanics. Disorder introduced by trading environment leads to probability distribution of returns…