Discussing quantum aspects of higher-derivative 3-D gravity in the first-order formalism

We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

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Quantum Ostrogradsky theorem

Journal of High Energy Physics ◽

10.1007/jhep09(2020)032 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Hayato Motohashi ◽

Teruaki Suyama

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Field ◽

First Order ◽

Higher Derivative ◽

Original Theorem ◽

Classical Lagrangian

Abstract The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

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Higher derivative fermionic field equation in the first-orderformalism

Canadian Journal of Physics ◽

10.1139/p07-083 ◽

2007 ◽

Vol 85 (8) ◽

pp. 887-897 ◽

Cited By ~ 3

Author(s):

S I Kruglov

Keyword(s):

Dirac Equation ◽

Spin Projection ◽

Electromagnetic Current ◽

Pure Spin ◽

Projection Operators ◽

Third Order ◽

First Order ◽

Generalized Dirac Equation ◽

Electromagnetic Interactions ◽

Higher Derivative

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first-order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found that extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and nonminimal(anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first-order equation is obtained.PACS Nos.: 03.65.Pm, 11.10.Ef; 12.10.Kt

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Generalized dualities and higher derivatives

Journal of High Energy Physics ◽

10.1007/jhep10(2020)002 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Tomas Codina ◽

Diego Marqués

Keyword(s):

Field Theory ◽

Heterotic Strings ◽

First Order ◽

Higher Derivative ◽

Double Field Theory ◽

Higher Derivatives

Abstract Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local O(d, d) transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.

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Supersymmetry, T-duality and heterotic α′-corrections

Journal of High Energy Physics ◽

10.1007/jhep07(2021)092 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Eric Lescano ◽

Carmen A. Núñez ◽

Jesús A. Rodríguez

Keyword(s):

Effective Field ◽

Heterotic String ◽

Supersymmetry Algebra ◽

Yang Mills ◽

First Order ◽

Duality Symmetry ◽

Transformation Rules ◽

Higher Derivative ◽

String Spectrum ◽

Fermionic Fields

Abstract Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $$ \mathcal{N} $$ N = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

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SOME QUANTUM ASPECTS OF THE REGULARIZATION WITH HIGHER DERIVATIVES

Modern Physics Letters A ◽

10.1142/s021773238900246x ◽

1989 ◽

Vol 04 (22) ◽

pp. 2195-2200 ◽

Cited By ~ 9

Author(s):

J. BARCELOS-NETO ◽

N.R.F. BRAGA

Keyword(s):

Canonical Quantization ◽

Scalar Theory ◽

Higher Derivative ◽

Higher Derivatives ◽

Quantum Aspects

We discuss the canonical quantization of scalar theory when higher derivative regulating terms are included in the Lagrangian.

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Faddeev-Jackiw quantization of the higher derivative Chern–Simons gauge theory in the first-order formalism

Chinese Journal of Physics ◽

10.1016/j.cjph.2021.06.002 ◽

2021 ◽

Author(s):

Jialiang Dai

Keyword(s):

Gauge Theory ◽

First Order ◽

Higher Derivative ◽

Chern Simons

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Eichler cohomology and zeros of polynomials associated to derivatives of L-functions

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2020-0011 ◽

2021 ◽

Vol 2021 (770) ◽

pp. 1-25

Author(s):

Nikolaos Diamantis ◽

Larry Rolen

Keyword(s):

Modular Forms ◽

Critical Role ◽

Cusp Forms ◽

Zeros Of Polynomials ◽

First Order ◽

Higher Derivative ◽

Eichler Cohomology ◽

Derivatives Of ◽

Special Case ◽

Function Field Case

Abstract In recent years, a number of papers have been devoted to the study of zeros of period polynomials of modular forms. In the present paper, we study cohomological analogues of the Eichler–Shimura period polynomials corresponding to higher L-derivatives. We state a general conjecture about the locations of the zeros of the full and odd parts of the polynomials, in analogy with the existing literature on period polynomials, and we also give numerical evidence that similar results hold for our higher derivative “period polynomials” in the case of cusp forms. The unimodularity of the roots seems to be a very subtle property which is special to our “period polynomials”. This is suggested by numerical experiments on families of perturbed “period polynomials” (Section 5.3) suggested by Zagier. We prove a special case of our conjecture in the case of Eisenstein series. Although not much is currently known about derivatives higher than first order ones for general modular forms, celebrated recent work of Yun and Zhang established the analogues of the Gross–Zagier formula for higher L-derivatives in the function field case. A critical role in their work was played by a notion of “super-positivity”, which, as recently shown by Goldfeld and Huang, holds in infinitely many cases for classical modular forms. As will be discussed, this is similar to properties which were required by Jin, Ma, Ono, and Soundararajan in their proof of the Riemann Hypothesis for Period Polynomials, thus suggesting a connection between the analytic nature of our conjectures here and the framework of Yun and Zhang.

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On perturbative aspects of a nonminimal Lorentz-violating QED with CPT-odd dimension-5 terms

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09768-4 ◽

2021 ◽

Vol 81 (11) ◽

Author(s):

T. Mariz ◽

R. Martinez ◽

J. R. Nascimento ◽

A. Yu. Petrov

Keyword(s):

Dimensional Regularization ◽

Regularization Scheme ◽

First Order ◽

Higher Derivative

AbstractWe consider the Lorentz-violating extended QED involving all nonminimal dimension-5 additive CPT-odd terms. For this theory, we investigate the generation of the Carroll–Field–Jackiw (CFJ) term and its higher-derivative counterparts of the first order in any of these nonminimal couplings. The CFJ term is demonstrated to vanish in the dimensional regularization scheme. We also study the question of higher-derivative divergent contributions and demonstrate that they can be eliminated by considering a given proportionality between the coefficients.

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