Related papers: Semiclassical Expansions, the Strong Quantum Limit…
This paper presents categorical structures on classical measure spaces and quantum measure spaces in order to deal with canonical maps associated with conditional measures as morphisms. We extend the Riesz-Markov-Kakutani representation…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
We consider anyonic excitations classified into equivalence classes labeled by Hausdorff dimension, $h$ and introduce the concept of duality between such classes, defined by $\tilde{h}=3-h$. In this way, we confirm that the filling factors…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
We analyze the framework recently proposed by Oppenheim et al. to model relativistic quantum fields coupled to relativistic, classical, stochastic fields (in particular, as a model of quantum matter coupled to ``classical gravity'').…
It is observed and illustrated in a greatly simplified example that the idea of AdS/QFT duality can be considered a special case of the Ehrenfest's correspondence principle between classical and quantum mechanics in the context of…
We treat the semiclassical Einstein equation as a quantum-classical hybrid and demonstrate the formal equivalence of its two derivation methods. This approach identifies the left-hand side of the equation as the expectation value of the…
We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, I analyze the qualitative…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Lectures given by C.G. in the Advanced School on Effective Theories (Almu\~{n}ecar, Granada, 1995) on duality in N=2 supersymmetric Yang-Mills, and the coupling to gravity.
We comment on the paper "Feynman Effective Classical Potential in the Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the results in this paper about the time evolution of a wave packet in a double well potential…
Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
A new idea of quantum gravity is developed based on {\it Gravitational Complementary Principle}. This principle states that gravity has dual complement features: The quantum and classical aspects of gravity are complement and absolutely…
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…
The results of the Young experiment can be analyzed either by classical or Quantum Physics. The later one though leads to a more complete interpretation, based on two different patterns that appear when one works either with single or…
We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…