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تسجيل مستخدم جديد$T{overline T}$ deformations and the width of fundamental particles
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We provide a simple geometric meaning for deformations of so-called $T{overline T}$ type in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories are known to modify the thermodynamic Bethe ansatz equations by a CDD factor. In turn, CDD factors may be interpreted as additional, fixed shifts incurred in scattering processes: a finite width added to the fundamental particles (or, if negative, to the free space between them). We suggest that this physical effect is a universal way of understanding $T{overline T}$ deformations, both in classical and quantum systems. We first show this in non-relativistic systems, with particle conservation and translation invariance, using the deformation formed out of the densities and currents of particles and momentum. This holds at the level of the equations of motion, and for any interaction potential, integrable or not. We then argue, and show by similar techniques in free relativistic particle systems, that $Toverline T$ deformations of relativistic systems produce the equivalent phenomenon, accounting for length contractions. We also show that, in both the relativistic and non-relativistic cases, the width of particles is equivalent to a state-dependent change of metric, where the distance function discounts the particles widths, or counts the additional free space. This generalises and explains the known field-dependent coordinate change describing $Toverline T$ deformations. The results connect such deformations with generalised hydrodynamics, where the relations between scattering shifts, widths of particles and state-dependent changes of metric have been established.
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$mathrm{T}overline{mathrm{T}}$ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which w
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We introduce an extension of the generalised $Tbar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary funct
ional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.
We point out that the arguments of Zamolodchikov and others on the $Toverline T$ and similar deformations of two-dimensional field theories may be extended to the more general non-Lorentz invariant case, for example non-relativistic and Lifshitz-type
theories. We derive results for the finite-size spectrum and $S$-matrix of the deformed theories.
In this paper, we continue the study of $Tbar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $Jbar{T}$ deformation and deformation by a general linear combination of $Tbar{T}$ and $Jbar{T}$ in quantum mechanics.
We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and $U(1)$ gauge theory.
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