Scalar, spinor, and photon fields under relativistic cavity motion

We analyze quantized scalar, spinor, and photon fields in a mechanically rigid cavity that is accelerated in Minkowski spacetime, in a recently introduced perturbative small-acceleration formalism that allows the velocities to become relativistic, with a view to applications in relativistic quantum information. A scalar field is analyzed with both Dirichlet and Neumann boundary conditions, and a photon field under perfect conductor boundary conditions is shown to decompose into Dirichlet-like and Neumann-like polarization modes. The Dirac spinor is analyzed with a nonvanishing mass and with dimensions transverse to the acceleration, and the MIT bag boundary condition is shown to exclude zero modes. Unitarity of time evolution holds for smooth accelerations but fails for discontinuous accelerations in spacetime dimensions ($3+1$) and higher. As an application, the experimental desktop mode-mixing scenario proposed for a scalar field by Bruschi et al. [New. J. Phys. 15, 073052 (2013)] is shown to apply also to the photon field.

Figure 1

Matching an inertial cavity to a uniformly accelerating cavity in ($1+1$)-dimensional Minkowski space, in the global Minkowski coordinates $(t,z)$. For $t\le 0$ the cavity is inertial, following the orbits of the time translation Killing vector ${\partial }_t$: the world lines of the walls are, respectively, $z=z_0$ and $z=z_1$, where $0<z_0<z_1$. For $t\ge 0$ the cavity is uniformly accelerated towards increasing $z$, in the sense that it follows the orbits of the boost Killing vector $z{\partial }_t+t{\partial }_z$: the world lines of the walls are, respectively, $z=\sqrt{z_0^2+t^2}$ and $z=\sqrt{z_1^2+t^2}$.

Figure 2

Behavior of the Bogoliubov coefficients for the massive ($1+1$)-dimensional Dirac field with MIT bag boundary conditions for increasing mass. The coefficient of $h$ in (6.23), denoted by ${\widehat{A}}_{{\Omega }_{k}l}(M)$, is plotted against the dimensionless combination $M≔\mu L$. Fig. 2a shows a selection of Bogoliubov coefficients that relate modes with the same sign of the frequency ($\alpha$-type coefficients): the map $k\mapsto n_k$ has been chosen so that $n_k\ge 0$ labels the positive frequency solutions and $n_k<0$ labels the negative frequency solutions. These mode-mixing coefficients are proportional to $M^2$ as $M\to \infty$. Figure 2b shows a selection of Bogoliubov coefficients that relate positive frequency modes with negative frequency modes ($\beta$-type coefficients). These particle creation coefficients are proportional to $M^{-6}$ as $M\to \infty$.