Related papers: Periods and Feynman amplitudes
We derive dispersion relations for $K\to\pi\pi$ decay, using the Lehmann-Symanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell…
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
A growing body of evidence suggests that the complexity of Feynman integrals is best understood through geometry. Recent mathematical developments [Kontsevich and Soibelman, arXiv:2402.07343] have illuminated the role of exponential…
As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities depend on the expansion of space and…
A long-standing conjecture in quantum field theory due to Broadhurst and Kreimer states that the amplitudes of the zig-zag graphs are a certain explicit rational multiple of the odd values of the Riemann zeta function. In this paper we…
The interface between classical physics and quantum physics is explained from the point of view of quantum information theory (Feynman Processes). The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of…
At a fundamental level every measurement process relies on an interaction where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interaction. This results in a…
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to…
The Riemann hypothesis is identified with zeros of ${\cal N}=4$ supersymmetric gauge theory four-point amplitude. The zeros of the $\zeta(s)$ function are identified with th complex dimension of the spacetime, or the dimension of the…
This papers deals with connections between quantum anomalies and transformations of Feynman pseudo-measures. Mathematical objects related to the notion of the volume element in an infinite-dimensional space considered in the physics…
It is argued that quantum propagation of D-particles in the limit \alpha'-> 0 can represent the "joining-splitting" processes of Feynman graphs of a certain field theory in the light-cone frame. So basically it provides the possibility to…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
We postulate that the Fermi function should be derived from the amplitude, not from the solution of the Dirac equation, in the quantum field theory. Then, we obtain the following results. 1, We give the amplitude and the width of the…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
With Grassmann algebra as fermions in a Feynman path-integral approach to field theory, the quantum correlation can be recovered. This means that a quantum field of Grassmann variables can explain the entanglement. In turn, this agrees with…
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
Various methods for the recursive evaluation of scattering amplitudes in quantum field theory and string theory have been put forward during the last couple of years. In these proceedings we describe a geometrical framework, which is…