Massive scalar field theory in the presence of moving mirrors

Abstract

We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding conjugate momentum in each case. We find that in case of the ideal mirror, which reflects modes with all momenta equally well, the commutation relations do not have their canonical form. However, in the case of non-ideal mirror, which is transparent for the modes with high enough momenta, the commutation relations of the field operator and its conjugate momentum have their canonical form. Then we calculate the free Hamiltonian and the expectation value of the stress-energy tensor in all the listed situations. In the presence of moving mirrors the diagonal form in terms of the creation and annihilation operators has the operator that performs translations along the mirror's world line rather than the one which does translations along the time-line. For the massive fields in the presence of a mirror moving with constant velocity the expectation value of the stress-energy tensor has a non-diagonal contribution which decays with the distance from the mirror.

Out of equilibrium two-dimensional Yukawa theory in a strong scalar wave background

“…Furthermore, the QFT in the background field Φ as given by eq. (3.1) is similar to the QFT in the presence of the non-ideal mirror [14], [15]. Such a mirror is transparent for high energy modes unlike the ideal one [16], [17], which reflects waves of any energy.…”

Quantization in background scalar fields

“…Second, usually loop integrals receive leading contributions due to large virtual momenta, q > p -the main income into the lower p-levels comes from the higher q-levels. Finally, the intuition gained during the study of other background fields [2,3,[6][7][8][9][10][11] tells us that the main contribution should come from the integrands of the form F * (t 3 )F (t 4 )e ip(t 3 −t 4 ) , because in this case it is possible to single out the part of the integrand which does not depend on t = t 3 +t 4 2 . (Then the integral over dt may give the growing with T factor.)…”

“…For instance, stationary approximation is violated in an expanding space-time (see e.g. [1][2][3][4][5]), in strong electric fields [6,7], during the gravitational collapse [8] and in a number of other non-trivial physical situations [9][10][11][12]. In such situations loop corrections to the tree-level correlation functions grow with time.…”

“…It would be interesting to calculate loop corrections to the quantum averages on top of such a rolling classical solution. In principle such corrections can change the situation under consideration [1][2][3][6][7][8][9][10][11]. If one considers a coherent state decay, most likely this would not happen: of course, strong initial perturbation can induce complex dynamics for a while, but one expects that eventually the field falls on the classical trajectory described by the equation (6.3) for large and slowly changing values of φ cl .…”

Time-Dependent Dissipative Massive Scalar Field

“…A dissipative scalar field with time-dependent damping factors can be used in describing time-dependent dissipative systems. Most of the physical systems are damping systems [7], [8].…”