Massive minimal subtraction scheme and “partial-pp” in anisotropic Lifshitz space(time)s

• “Partial–p” operation introduced for anisotropic Lifshitz spaces.
• Massive minimal subtraction framework utilizing counterterms generated iteratively.
• Application: Determination of critical indices.
• Equivalence of the exponents with other schemes.
• Rigorous mathematical consistency of the orthogonal approximation.

We introduce the “partial-pp” operation in a massive Euclidean λϕ4λϕ4 scalar field theory describing anisotropic Lifshitz critical behavior. We then develop a minimal subtraction a la Bogoliubov–Parasyuk–Hepp–Zimmermann renormalization scheme. As an application we compute critical exponents diagrammatically using the orthogonal approximation at least up to two-loop order and show their equivalence with other renormalization techniques. We discuss possible applications of the method in other field-theoretic contexts.