اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSymplectic quantization I: dynamics of quantum fluctuations in a relativistic field theory
151
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This proper time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in the companion work Symplectic quantization II.
قيم البحث
اقرأ أيضاً
The symplectic quantization scheme proposed for matter scalar fields in the companion paper Symplectic quantization I is generalized here to the case of space-time quantum fluctuations. Symplectic quantization considers an explicit dependence of the
metric tensor $g_{mu u}$ on an additional time variable, named proper time at variance with the coordinate time of relativity. The physical meaning of proper time is to label the sequence of $g_{mu u}$ quantum fluctuations at a given point of the four-dimensional space-time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative $dot{g}_{mu u}$ of the metric field with respect to proper time, corresponding to the conjugated momentum $pi_{mu u}$. Symplectic quantization describes the quantum fluctuations of gravity by means of the symplectic dynamics generated by a generalized action functional $mathcal{A}[g_{mu u},pi_{mu u}] = mathcal{K}[g_{mu u},pi_{mu u}] - S[g_{mu u}]$, playing formally the role of a Hamilton function, where $S[g_{mu u}]$ is the Einstein-Hilbert action and $mathcal{K}[g_{mu u},pi_{mu u}]$ is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define a pseudo-microcanonical ensemble for the quantum fluctuations of $g_{mu u}$, built on the conservation of the generalized action $mathcal{A}[g_{mu u},pi_{mu u}]$ rather than of energy. $S[g_{mu u}]$ plays the role of a potential term along the symplectic action-preserving dynamics: its fluctuations are the quantum fluctuations of $g_{mu u}$. It is shown how symplectic quantization maps to the path-integral approach to gravity. By doing so we explain how the integration over the conjugated momentum field $pi_{mu u}$ gives rise to a cosmological constant term in the path-integral.
We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R{e}nyi entropy of such states and recover the Ryu-Takayanagi for
mula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.
Einstein equations projected on to a black hole horizon gives rise to Navier-Stokes equations. Horizon-fluids typically possess unusual features like negative bulk viscosity and it is not clear whether a statistical mechanical description exists for
such fluids. In this work, we provide an explicit derivation of the Bulk viscosity of the horizon-fluid based on the theory of fluctuations a la Kubo. The main advantage of our approach is that our analysis remains for the most part independent of the details of the underlying microscopic theory and hence the conclusions reached here are model independent. We show that the coefficient of bulk viscosity for the horizon-fluid matches exactly with the value found from the equations of motion for the horizon-fluid.
We describe the evolution of slowly spinning compact objects in the late inspiral with Newtonian corrections due to spin, tides, dissipation and post-Newtonian corrections to the point mass term in the action within the effective field theory framewo
rk. We evolve the system numerically using a simple algorithm for point particle simulations and extract the lowest-order Newtonian gravitational waveform to study its phase evolution due to the different effects. We show that the matching of coefficients of the effective field theory for compact objects from systems that the gravitational wave observatories LIGO-Virgo currently detects might be possible and it can place tight constraints on fundamental physics.
We study relativistic anyon field theory in 1+1 dimensions. While (2+1)-dimensional anyon fields are equivalent to boson or fermion fields coupled with the Chern-Simons gauge fields, (1+1)-dimensional anyon fields are equivalent to boson or fermion f
ields with many-body interaction. We derive the path integral representation and perform the lattice Monte Carlo simulation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
