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Klaus Bering

Publications and source records attributed to Klaus Bering.

At least 19 recordsLinked to original sources
arXiv2025

A Note on Instantons in a 1D Same-Level Asymmetric Double Well

We prove formulas for the multi-instanton corrections to the overlap and energies of a 1D same-level asymmetric double well using the Euclidean path integral. Both the odd and even instanton sectors are summed to all orders. The double well is same-level asymmetric in the sense that the potentials at neighboring wells have the same bottom level but can have different Hessians/curvatures/frequencies, which modify Coleman's original formulas. This for instance implies that the reference model used to calculate the functional determinant of quantum fluctuations must now interpolate between simple harmonic oscillators of different frequencies. Examples of symmetric double and triple wells are worked out.

quant-ph↗
arXiv2022

Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D

We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D $\mathcal{N}=4$ SYM, and therefore we consider a 6D Grassmannian formula, where we can take advantage of massless kinematics. We next use symmetry arguments, and in particular, 6D dual conformal symmetry generalized to arbitrary dual conformal weights. Assuming a rational ansatz in terms of Plücker coordinates (i.e. minors) for the integrand, this approach leads to a set of algebraic equations. As an example, we explicitly find the solution for 4-point scattering amplitudes up to proportionality constants.

hep-th↗
arXiv2022

A note on tree factorization and no particle production

We prove factorization of the generating functional of connected tree diagrams by exploring that it is the Legendre transform of the action. This theorem is then applied to the example of a massive real scalar field theory in 2D. In the process we streamline the proof that the assumption of no particle production leads to either the sin(h)-Gordon or the Bullough-Dodd model.

hep-th↗
arXiv2021

Generalized Jarlskog Invariants, Mass Degeneracies and Echelon Crosses

It is known that the Cabibbo-Kobayashi-Maskawa (CKM) $n\times n$ matrix can be represented by a real matrix iff there is no CP-violation, and then the Jarlskog invariants vanish. We investigate sufficient conditions for the opposite statement to hold, paying particular attention to degenerate cases. We find that higher Jarlskog invariants are needed for $n\geq 4$. One generic sufficient condition is provided by the existence of a so-called echelon cross.

hep-th↗
arXiv2020

6D dual superconformal algebra

We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D $\mathcal{N}=4$ SYM and extends the previous construction of the enhanced dual conformal algebra for 6D $\mathcal{N}=(1,1)$ SYM to the full 6D dual superconformal algebra for chiral theories. We formulate constraints in 6D spinor helicity formalism and find all generators of the 6D dual superconformal algebra. Next we check that they agree with the dual superconformal generators of known 3D and 4D theories. We show that it is possible to significantly simplify the form of generators and compactly write the dual superconformal algebra using superindices. Finally, we work out some examples of algebra invariants.

hep-th↗
arXiv2020

Multiplicative renormalizability of Yang-Mills theory with the background field method in the BV-formalism

Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV-formalism, we derive a classical master-equation homogeneous with respect to the antibracket by introducing antifield partners to the background fields and parameters. The constructed model can be renormalized by the standard method of introducing counterterms. This model does not have (exact) multiplicative renormalizability but it does have this property in the physical sector (quasimultiplicative renormalizability).

hep-th↗
arXiv2016

A systematic study of finite BRST-BV transformations within W-X formulation of the standard and the Sp(2)-extended field-antifield formalism

Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived.

hep-th↗
arXiv2014

External Sources in Field-Antifield Formalism

We introduce external sources J_A directly into the quantum master action W of the field-antifield formalism instead of the effective action. The external sources J_A lead to a set of BRST-invariant functions W^A that are in antisymplectic involution. As a byproduct, we encounter quasi--groups with open gauge algebras.

hep-th↗
arXiv2012

Non-Decomposable Nambu Brackets

It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e., given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein's splitting principle for Poisson manifolds.

math-ph↗
arXiv2012

A Triplectic Bi-Darboux Theorem and Para-Hypercomplex Geometry

We provide necessary and sufficient conditions for a bi-Darboux Theorem on triplectic manifolds. Here triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the manifold dimension. By definition bi-Darboux coordinates are common Darboux coordinates for two Poisson brackets. We discuss both the Grassmann-even and the Grassmann-odd Poisson bracket case. Odd triplectic manifolds are, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence between triplectic manifolds and para-hypercomplex manifolds. Existence of bi-Darboux coordinates on the triplectic side of the correspondence translates into a flat Obata connection on the para-hypercomplex side.

math-ph↗
arXiv2012

A Note on Angular Momentum Commutators in Light-Cone Formulation of Open Bosonic String Theory

We recalculate in a systematic and pedagogical way one of the most important results of Bosonic open string theory in the light-cone formulation, namely the [J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously yield the critical dimension D=26 and the normal order constant a=1. We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter κto avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.

hep-th↗
arXiv2011

Noether's Theorem for a Fixed Region

We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global quasi-symmetry.

math-ph↗
arXiv2011

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.

physics.optics↗