Energies of the strongly-dissipative quantum scalar field

Abstract Dynamics and energies of a quantum dissipative scalar field at finite temperature and in strong-coupling regime are investigated. The Lagrangian of the total system is canonically quantized and symmetric correlation functions are obtained. To employ the thermo-field technique, the density operator of the strongly dissipative scalar field is introduced. Mean energy, internal energy, and thermally averaged energy of the system are calculated. Also, mean energy and internal energy are written in terms of probability distribution function in frequency domain that is shown the energy functions satisfy the quantum counterpart of the energy equipartition theorem. In the weak coupling regime, all the energy expressions reduce to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>ℏ</mml:mi> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mi>coth</mml:mi> <mml:mo>⁡</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>ℏ</mml:mi> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>K</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> <mml:mi>T</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , that is the familiar result.