Ashok K. Das, J. Frenkel
Using the closed time path formalism in thermal field theory, we give a derivation of the fluctuation-dissipation theorem which is based on the unitarity of the $S$-matrix.
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The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and thus can be considered as in local equilibrium. For a many-body system in local equilibrium a stronger version of the second law applies which says that the entropy production at each spacetime point should be non-negative. In this paper we provide a proof of the second law for such systems and a first derivation …
Motivated by a recent work by Terashima (Phys. Rev. D60 084001), we revisit the fluctuation-dissipation (FD) relation between the dissipative coefficient of a detector and the vacuum noise of fields in curved spacetime. In an explicit manner we show that the dissipative coefficient obtained from classical equations of motion of the detector and the scalar (or Dirac) field satisfies the FD relation associated with the vacuum noise of the field, which demonstrates that the Terashima's prescription works properly in the $N$-dimensional de Sitter spacetime. This practice is useful not only to reco…
We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demo…
We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian.…
Higher-Derivative Quantum Gravity with Purely Virtual Particles: Renormalizability and Unitarity
本文回顾了含纯虚粒子的量子场论，展示了其如何解决高阶导数量子引力中的鬼场问题，从而获得可重整且幺正的理论，并给出了暴胀宇宙学中的唯象预言。
We revisit the problem of deriving local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory. Previous derivations were based on the condition of tree-order unitarity. However, the modern point of view considers the Standard Model as the leading order approximation to an effective field theory. As tree-order unitarity is in any case violated by higher-order terms in an effective field theory, it is instructive to investigate a formalism which can be also applied to analyze higher-order interactions. In the current work we consider an effective field …
Microscopic Unitarity and the Quantization of Black Hole Evaporation Time
本文提出一个微观单位性框架，通过全息原理限制信息通道熵，推导出量子条件以实现黑洞蒸发时间的量化。
Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough …
The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with …
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topologi…
The most striking result here is that the notion of Planckian dissipation is also applicable to the $c$-axis resistivity of the high temperature cuprate superconductors, and to my knowledge this aspect has not been previously addressed. The derivation involves Kubo formula and does not require any mechanism beyond a non-Fermi liquid assumption. The $c$-axis resistivity, in its essential aspects, is discussed in the context of quantum critical point. Finally, I consider a zero temperature problem with one of its spatial dimensions compactified. The warning is that this compatification scale at …
In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. Here, we discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is a…
There has been a recent interest in considering Quantum Field Theories in which Lorentz Invariance is broken in the UV sector. However attention has been mostly limited to dispersive theories. In this work we provide the generalized settings for studying dissipation. Unitarity is preserved by coupling the original fields to additional (heavy) fields which induce the dissipation. Starting with Lagrangians breaking LI in the UV, we learn that dissipative effects unavoidably develop in the effective theory. We then covariantize these Lagrangians in order to address the trans-Planckian question of…
Positivity-causality competition: a road to ultimate EFT consistency constraints
本文通过比较幺正性正性约束与低能因果性条件，证明二者互补且联合应用可显著缩小光子有效场论的参数允许区域。
At the physical level of rigour it is shown that there are no substantial theoretical arguments in favour of using either plasma mode permittivity or Drude model permittivity in the Lifshitz formula. The decision in this question rests with the comparison of theoretical calculations with the experiment. In the course of the study the derivation of the fluctuation-dissipation theorem is proposed where it is displayed clear at which reasoning stage and in what way the dissipation is taken into account. In particular it is shown how this theorem works in the case of the system with reversible dyn…
We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the Equivalence Principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator mad…
Black Hole Thermodynamics Meets On-Shell Amplitudes: Local Detailed Balance and Thermal Spectrum from Spin Universality and Unitarity
提出一个用于宏观物体热耗散和辐射的壳上框架，通过自旋普适性和幺正性推导出局部细致平衡和热谱，并应用于黑洞得到霍金温度。
The unitarity of time evolution, or colloquially the conservation of probability, sits at the heart of our descriptions of fundamental interactions via quantum field theory. The implications of unitarity for scattering amplitudes are well understood, for example through the optical theorem and cutting rules. In contrast, the implications for in-in correlators in curved spacetime and the associated wavefunction of the universe, which are measured by cosmological surveys, are much less transparent. For fields of any mass in de Sitter spacetime with general local interactions, which need not be i…
The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the …
While the issues of dissipation, fluctuations, noise and decoherence in open quantum systems (with autocratic divide) analyzed via Langevin dynamics are familiar subjects, the treatment of corresponding issues in closed quantum systems is more subtle, as witnessed by Boltzmann's explanation of dissipation in a macroscopic system made up of many equal constituents (a democratic system). How to extract useful physical information about a closed democratic system with no obvious ways to distinguish one constituent from another, nor the existence of conservation laws governing certain special kind…
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