Renormalization in open quantum field theory. Part I. Scalar field theory

Baidya, Avinash; Jana, Chandan; Loganayagam, R.; Rudra, Arnab

doi:10.1007/jhep11(2017)204

Cited by 37 publications

(68 citation statements)

References 40 publications

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“…This condition is based on the Hermiticity of the operator q(t) which implies that the correlators of q should remain unchanged under a reversal of the ordering of the insertions followed by a complex conjugation. As discussed in [45,51], the above reality conditions ensure that such relations between the particle's correlators are satisfied. 12 It is important to keep this regulator as otherwise one can get wrong answers while computing contributions of loop diagrams where two of the q's on the same vertex contract with each other.…”

Section: • Reality Conditionsmentioning

confidence: 92%

“…As discussed in [5,45,51], this condition is based on the fact that the particle is a part of a closed system governed by a unitary dynamics. At the level of correlators, it makes sure that the value of a contour-ordered correlator of the particle just picks up a sign when one slides the future-most insertion from one leg to the other without changing its temporal position.…”

Section: • Collapse Rulementioning

confidence: 99%

“…At the level of correlators, it makes sure that the value of a contour-ordered correlator of the particle just picks up a sign when one slides the future-most insertion from one leg to the other without changing its temporal position. The sign is introduced because we are putting an extra minus sign in the definition of q 2 over the convention followed in [5,51].…”

Section: • Collapse Rulementioning

confidence: 99%

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Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

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We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle. Contents SciPost PhysicsSubmission [22,[27][28][29]. Nevertheless, it is interesting to explore the corrections to this effective dynamics by including the cubic and higher degree terms in the analysis. A simple way to obtain such corrections is to extend the Caldeira-Leggett model by introducing a non-linear combination of the bath oscillators' positions in the operator that couples to the particle [29,30].One such extension was discussed in [30] where the oscillators in the bath were divided into two sets (labelled by X and Y). Then apart from the bilinear interactions (which are present in the Caldeira-Leggett model), small cubic interactions were introduced between the particle (q) and pairs of bath oscillators. Each such pair consisted of one oscillator drawn from the set X and the other from the set Y. Due to these cubic interactions, this model was called the 'qXY model'.Introduction of these cubic interactions leads to cubic and higher degree terms in the effective action of the particle. In [30], this effective theory was studied up to the cubic terms in a Markovian limit. It was shown to be dual to a non-linear Langevin dynamics which has perturbative corrections over the linear Langevin dynamics in the Caldeira-Leggett model. The additional parameters in this non-linear dynamics receive contributions from the 3-point correlators of the bath. These 3-point correlators lead to an anharmonicity in the particle's dynamics and a non-Gaussianity in the distribution of the thermal noise experienced by the particle. In addition, they also give rise to thermal jitters 1 in both the frequency and the damping of the particle. The thermal jitter in the damping coefficient and the non-Gaussianity in the noise are connected by a generalised fluctuation-dissipation relation [30...

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Section: • Reality Conditionsmentioning

confidence: 92%

Section: • Collapse Rulementioning

confidence: 99%

Section: • Collapse Rulementioning

confidence: 99%

See 1 more Smart Citation

Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

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“…This condition is necessary for the heavy quark's correlators to satisfy the largest time equation. This condition is also responsible for the Lindblad structure of master equation obeyed by the heavy quark's density matrix [44,45].…”

Section: B Heavy Quark In Sk Formalismmentioning

confidence: 99%

“…The coefficient functions G[a 2 ] and G[a 4 ] vanish by arguments analogous to those given for the vanishing of G[PP], G[FF], G[PPPP] and G[FFFF] in the previous subsection. The absence of the corresponding terms in the influence phase implies that the master equation that evolves the quark's density matrix has a Lindblad form [8,45].…”

Section: B Influence Phase In Keldysh Basis and Its Derivative Expanmentioning

confidence: 99%

Nonlinear Langevin dynamics via holography

Chakrabarty

Chakravarty

Chaudhuri

et al. 2020

J. High Energ. Phys.

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In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence functional for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime. Contents

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Ghostbusters: unitarity and causality of non-equilibrium effective field theories

Gao¹,

Glorioso

Liu

2020

J. High Energ. Phys.

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For a non-equilibrium physical system defined along a closed time path (CTP), a key constraint is the so-called largest time equation, which is a consequence of unitarity and implies causality. In this paper, we present a simple proof that if the propagators of a non-equilibrium effective action have the proper pole structure, the largest time equation is obeyed to all loop orders. Ghost fields and BRST symmetry are not needed. In particular, the arguments for the proof can also be used to show that if ghost fields are introduced, their contributions vanish.

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Renormalization in open quantum field theory. Part I. Scalar field theory

Cited by 37 publications

References 40 publications

Out of time ordered effective dynamics of a quartic oscillator

Out of time ordered effective dynamics of a quartic oscillator

Nonlinear Langevin dynamics via holography

Ghostbusters: unitarity and causality of non-equilibrium effective field theories

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