Despite the large amount of work done in quantum field theory in curved space-times, there are not great many results available for perturbative calculations of particle processes in these systems. Such processes are expected to be important in the early stages of the universe, as well as near highly relativistic objects like black holes and, recently, in effective field theories of condensed matter systems. The difficulties with carrying out perturbative calculations in curved space-times are related to the practical difficulty of quantizing in curved space-times. This suggests the need for investigating new approximations and comparing the results of different methods of carrying out the calculations. In this paper, we compare different perturbative approaches to particle scattering problems and illustrate them with examples. In particular, we look at a 1+1 dimensional static spacetime. We also examine the spacetime particle generation in a 1+1 Robertson-Walker universe, where we find that the curved space LSZ formula yields new information compared to the in-in formalism.
String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the closed bosonic sector of string geometry theory, we derive path integrals of all order perturbative strings on all the string backgrounds, $G_{μν}(x)$, $B_{μν}(x)$, and $Φ(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.
Gravity curves spacetime. In regions where the de Broglie wavelength is very small compared to the curvature of spacetime, the wave equations in flat spacetime can be generalized to curved spacetime. The validity of the formulation when the de Broglie wavelength becomes comparable to the curvature is an open question. To test these formulations experimentally, huge energy of the order of the Planck mass would be required. Euclideanized spacetime is used to model thermal systems. In this work, an equivalence between spatial variation of temperature in thermal baths and curvature of Euclideanize…
The success of the S-matrix in quantum field theory in Minkowski spacetime naturally demands the extension of the construction of the S-matrix in a general curved spacetime in a covariant manner. However, it is well-known that a global description of the S-matrix may not exist in an arbitrary curved spacetime. Here, we give a local construction of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinates which mimics the methods, generally used in Minkowski spacetime. Using this construction, the scattering amplitudes and cross-sections of some scattering processes …
This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about quantum field theory in curved spacetime and about the thermodynamic limit of quantum statistical mechanics. We also briefly explain that these results have an analog in the large N limit of gauge theory.
Nonperturbative stochastic inflation in perturbative dynamical background
Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of [Phys. Rev. D 22, 1922]. Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schrödinger equation assoc…
This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-$j$ Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude.…
我们研究非对易弯曲时空上的经典标量场理论。遵循Wess等人[Classical量子引力22（2005），3511 and Classical量子引力23（2006），1883]的方法，我们用（阿贝尔）Drinfel'd扭曲和相关的 *-乘积和 *-微分几何描述非对易时空。特别是，我们允许位置相关的非交换性，并不限制自己的Moyal-Weyl变形。构造了非对易弯曲时空上实标量场的作用泛函，并导出了相应的变形波动方程。我们提供了明确的例子变形Klein-Gordon运营商的非对易闵可夫斯基，德西特，史瓦西和兰德尔Sundrum时空，解决非对易爱因斯坦方程。我们研究了变形格林函数的构造，并提供了一个图形化的微扰计算方法。我们的例子中的格林函数的领先的非交换修正。
We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of prev…
In this work, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a 4D curved space-time, the generalization of a cosmic string space-time. We investigate the Klein-Gordon equation in the presence of external fields in the considered framework. We also investigate a quantum particle described by the Klein-Gordon oscillator in the curved background space-time in the presence of external fields. We see that the energy eigenvalues get modifies in comparison to the results obtained in a cosmic string space-time.
A general formalism of the spin quantum entanglement in a curved space-time represented. As examples Kerr and non commutative Reissner- Nordström models are considered. The behaviors of the concurrence and entanglement entropy as a function of the various parameters are also discussed.
We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time…
