Related papers: Duality in Perturbation Theory and the Quantum Adi…
We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO-orientation of L-theory…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms…
A formulation of quantum electrodynamics is given that applies to atoms in a strong laser field by perturbation theory in a non-relativistic regime. Dipole approximation is assumed. The dual Dyson series, here discussed by referring it to…
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
Quantum mechanically, a driving process is expected to be reversible in the quasistatic limit, also known as the adiabatic theorem. This statement stands in opposition to classical mechanics, where a mix of regular and chaotic dynamics…
These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the…
Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…
A certain two-dimensional supersymmetric gauge theory is argued to satisfy a relation that promotes the Zamolodchikov tetrahedron equation to an infrared duality between two quantum field theories. Solutions of the tetrahedron equation with…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
Wave-particle duality relations express the fact that knowledge about the path a particle took suppresses information about its wave-like properties, in particular, its ability to generate an interference pattern. Recently, duality…
The classical duality theory associates to an abelian group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…