  This paper describes the canonical quantization of the U(1) gauge field
across all four regions in the Rindler coordinates in the Lorentz covariant
gauge. In the four regions (future, past, left and right Rindler-wedges) in the
Rindler coordinates, defining the gauge-fixed Lagrangian in the Lorentz
covariant gauge, which is composed of the U(1) gauge field, the $B$-field and
ghost fields. Since the U(1) gauge and $B$-fields are decoupled from the ghost
fields by the property of the U(1) gauge theory, the U(1) gauge field and the
$B$-field are examined in this study.
  Then, by solving the equations of motion obtained from the gauge-fixed
Lagrangian, the solutions of each mode of the U(1) gauge field and the
$B$-field can be obtained. Following this, with the Klein-Gordon inner-product
defined in the Rindler coordinates, the normalization constants of each of
those mode-solutions are determined.
  Subsequently, formulating the canonical commutation relations of the U(1)
gauge field and its canonical conjugate momentum, the commutation relations of
the coefficient of each mode-solution in each direction of the U(1) gauge field
in each region of the Rindler coordinates are obtained. From these, it can be
seen that those coefficients have physical meaning as creation/annihilation
operators. The polarization vectors in each region of the Rindler coordinates
are also given in this study.
  From these, it is shown that the Minkowski ground state can be given as the
outer-product of the quantum states multiplied by the creation operators of the
U(1) gauge field in the left and right Rindler-wedge states.
  Then, obtaining the density matrix of the U(1) gauge theory in the right
Rindler-wedge from that, it is shown that the U(1) gauge field in the constant
accelerated system feels the Unruh temperature as well.
