arXiv subjects

F. G. Scholtz

Publications and source records attributed to F. G. Scholtz.

30 records · Page 2Linked to original sources

arXiv2004

Non-perturbative flow equations from continuous unitary transformations

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving one flow parameter and two system specific auxiliary variables. The implementation is non-perturbative as the partial differential equation involves a systematic expansion in fluctuations, controlled by the size of the system, rather than the coupling constant. The method is applied to the Lipkin model to construct a mapping which maps the non-interacting spectrum onto the interacting spectrum to a very high accuracy. This function is universal in the sense that the full spectrum for any (large) number of particles can be obtained from it. In a similar way expectation values for a large class of operators can be obtained, which also makes it possible to probe the stucture of the eigenstates.

cond-mat.other↗

arXiv2004

Revisiting the Fradkin-Vilkovisky Theorem

The status of the usual statement of the Fradkin-Vilkovisky theorem, claiming complete independence of the Batalin-Fradkin-Vilkovisky path integral on the gauge fixing "fermion" even within a nonperturbative context, is critically reassessed. Basic, but subtle reasons why this statement cannot apply as such in a nonperturbative quantisation of gauge invariant theories are clearly identified. A criterion for admissibility within a general class of gauge fixing conditions is provided for a large ensemble of simple gauge invariant systems. This criterion confirms the conclusions of previous counter-examples to the usual statement of the Fradkin-Vilkovisky theorem.

hep-th↗

arXiv2003

Observation of Exceptional Points in Electronic Circuits

Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points -- connecting dissipation with spatial orientation -- concludes the paper.

quant-ph↗

arXiv2001

Effective field theories for disordered systems from the logarithmic derivative of the wave-function

We consider a spinless particle moving in a random potential on a d-dimensional torus. Introducing the gradient of the logarithm of the wave-function transforms the time independent Schroedinger equation into a stochastic differential equation with the random potential acting as the source. Using this as our starting point we write functional integral representations for the disorder averaged density of states, the two point correlator of the absolute value of the wave-function as well as the conductivity for a d-dimensional system. We use the well studied one dimensional system with Gaussian disorder to illustrate that these quantities can be computed reliably in the current formalism by using standard approximation techniques. We also indicate the possibility of including magnetic fields.

cond-mat.dis-nn↗

arXiv1998

Thermal Bosonic and Fermionic Quantum Fields in Static Background Gauge Potentials

We study at finite temperature the energy-momentum tensor $T_{μν}(x)$ of (i) a scalar field in arbitrary dimension, and (ii) a spinor field in 1+1 dimensions, interacting with a static background electromagnetic field. $T_{μν}$ separates into an UV divergent part $T_{μν}^{sea}$ representing the virtual sea, and an UV finite part $T_{μν}^{plasma}$ describing the thermal plasma of the matter field. $T_{μν}^{sea}$ remains uniform in the presence of a \underbar{uniform} electric field $\vec E$, while $T_{μν}^{plasma}$ becomes a periodic function with period $Δx=2πT/E$ in the direction parallel to $\vec E$. A related periodicity is found for a uniform static magnetic field if one spatial direction perpendicular to the magnetic field is compactified to a circle.

hep-th↗

arXiv1997

Decoupled path integral formulation of chiral QCD$_2$ with $a_{JR}=2$

We analyse the BRST constraints and corresponding Hilbert-space structure of chiral QCD$_2$ in the decoupled formulation for the case of the Jackiw-Rajaraman parameter $a=2$. We show that despite formal similarities this theory is not equivalent to QCD$_2$, and that its extension to U(N) does not lead to an infinite vacuum degeneracy.

hep-th↗

arXiv1996

BRST Cohomology and Hilbert Spaces of Non-Abelian Models in the Decoupled Path Integral Formulation

The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of simple quantum mechanical and field theoretical models, where the structure of the Hilbert space is known. We provide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equivalence of the decoupled formulation to the original, coupled one.

hep-th↗

arXiv1996

Supersymmetric quantization of Yang-Mills theory and possible applications

We develop a new operator quantization scheme for gauge theories where no gauge fixing for gauge fields is needed. The scheme allows one to avoid the Gribov problem and construct a manifestly Lorentz invariant path integral that can be used in the non-perturbative domain. We discuss briefly an application of the method to Abelian projections of QCD.

hep-th↗

arXiv1994

Spin in the path integral: anti-commuting versus commuting variables

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a `free field realization' (Dyson mapping) can be constructed in the path integral.

hep-th↗

arXiv1994

Non-abelian bosonization from factored coset models in path integrals

We present a derivation of abelian and non-abelian bosonization in a path integral setting by expressing the generating functional for current-current correlation functions as a product of a $G/G$-coset model, which is dynamically trivial, and a bosonic part which contains the dynamics. A BRST symmetry can be identified which leads to smooth bosonization in both the abelian and non-abelian cases.

hep-th↗

arXiv1994

Loosely bound hyperons in the SU(3) Skyrme model

Hyperon pairs bound in deuteron like states are obtained within the SU(3) Skyrme model in agreement with general expectations from boson exchange models. The central binding from the flavor symmetry breaking terms increases with the strangeness contents of the interacting baryons whereas the kinetic non-linear $σ$-model term fixes the spin and isospin of the bound pair. We give a complete account of the interactions of octet baryons within the product approximation to baryon number $B=2$ configurations.

nucl-th↗

arXiv1993

Boson-fermion mappings for odd systems from supercoherent states

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2$N$+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.

nucl-th↗