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We apply the quartic exponential variational approximation to the symmetrybreaking phenomena of scalar field in three and four dimensions. We calculateeffective potential and effective action for the time-dependent system byseparating the zero mode from other non-zero modes of the scalar field andtreating the zero mode quantum mechanically. It is shown that the quantummechanical properties of the zero mode play a non-trivial role in the symmetrybreaking of the scalar $\lambda \phi^4$ theory.Comment: 10 pages, 3 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Zero mode in the time-dependent symmetry breaking of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory

Zero mode in the time-dependent symmetry breaking ofλφ4theory