Related papers: Weak value picture on quantum observables: gauge-i…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a…
Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experimental results of varying fine structure constant,obtained from many-multiplet Quaser absorption systems and atomic clocks.The variation of that…
Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics.…
The dynamics of a molecule in a magnetic field is significantly different form its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of…
A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the…
The canonical commutation relations in quantum mechanics are not maintained in the anomalous Hall effect described by Berry's phase in the presence of the electromagnetic vector potential. To define quantum mechanical formulation, one may…
The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the…
In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…
Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in $N$-dimensional quantum systems in…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…