Connoisseurs of sound and the new formalism

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

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Solution of tetrahedron equation and cluster algebras

Journal of High Energy Physics ◽

10.1007/jhep05(2021)103 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

P. Gavrylenko ◽

M. Semenyakin ◽

Y. Zenkevich

Keyword(s):

Integrable System ◽

Cluster Algebra ◽

Newton Polygon ◽

Cluster Algebras ◽

Weyl Groups ◽

Newton Polygons ◽

Tetrahedron Equation ◽

Affine Weyl Groups ◽

New Formalism ◽

Bruhat Cell

Abstract We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism, we show how to construct an integrable system with the spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into the double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to the general non-symmetric Newton polygons, and prove the Lemma which classifies conjugacy classes in double affine Weyl groups of A-type by decorated Newton polygons.

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The Weyl double copy from twistor space

Journal of High Energy Physics ◽

10.1007/jhep05(2021)239 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Erick Chacón ◽

Silvia Nagy ◽

Chris D. White

Keyword(s):

Exact Solutions ◽

Twistor Space ◽

Current Form ◽

New Formalism ◽

Petrov Types ◽

Gravity Theories ◽

Double Copy

Abstract The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as well as self-dual fields, and clarify some conceptual issues in the twistor approach.

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A New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194516600983 ◽

2016 ◽

Vol 40 ◽

pp. 1660098

Author(s):

K. Heinemann ◽

D. P. Barber ◽

J. A. Ellison ◽

M. Vogt

Keyword(s):

Normal Form ◽

Spin Dynamics ◽

Invariant Sets ◽

Spin Orbit ◽

Spin Tensor ◽

Spin Vector ◽

Spin Motion ◽

New Formalism ◽

Fibre Bundles ◽

Ongoing Work

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties invariant fields with the notion of normal form, the second allows comparison of different invariant fields and the two others tie the existence of invariant fields to the existence of certain invariant sets. We explain how the theorems apply to the spin dynamics of spin-[Formula: see text] and spin-[Formula: see text] particles. Our approach elegantly unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics and suggests an avenue for addressing the question of the existence of the invariant spin field.

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New formalism for the study of lattice Hamiltonians

Physical Review B ◽

10.1103/physrevb.41.4377 ◽

1990 ◽

Vol 41 (7) ◽

pp. 4377-4388 ◽

Cited By ~ 6

Author(s):

R. S. Fishman

Keyword(s):

New Formalism

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New formalism for bending losses in coated single-mode optical fibres

Electronics Letters ◽

10.1049/el:19891038 ◽

1989 ◽

Vol 25 (22) ◽

pp. 1544 ◽

Cited By ~ 26

Author(s):

I. Valiente ◽

C. Vassallo

Keyword(s):

Single Mode ◽

Optical Fibres ◽

New Formalism ◽

Bending Losses

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Chiral perturbation theory for GR

Journal of High Energy Physics ◽

10.1007/jhep09(2020)017 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Kirill Krasnov ◽

Yuri Shtanov

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation ◽

Perturbative Calculation ◽

New Formalism ◽

Yang Mills ◽

First Order ◽

Starting Point ◽

Gauge Fixing ◽

New Perturbation ◽

Effective Description

Abstract We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

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