Related papers: Generalized Unitarity Relation for Linear Scatteri…
Scattering properties and time delays for general (non-symmetric) potentials in terms of the respective S-matrices are discussed paradigmatically in one dimension and in comparison to symmetric potentials. Only for the latter the Wigner and…
Investigations of scattering in presence of non-linearity which have just begun require the confinement of both the potential, $V(x)$, and the non-linearity, $\gamma f(|\psi|)$. There could be two options for the confinement. One is the…
The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative…
We present a theory of cooperative light scattering valid in any dimension: connecting theories for an open line, open plane, and open space in the non-relativistic regime. This theory includes near-field and dipole-orientation effects,…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies…
In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent…
In understanding the world of matter, the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear…
Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly continuous with respect to a distance predicate. Every general…
Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…
Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory.…
Unitarity imposes coupled constraints on elastic and inelastic amplitudes. Satisfying them requires resummation of the self-energy contributions from both elastic and inelastic channels. Inelastic channels generate anti-Hermitian…
Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of…
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered.…