- The paper presents significant improvements in tensor reduction, enabling efficient decomposition of one-loop integrals using a generalized Passarino-Veltman framework.
- It introduces a robust partial fractioning algorithm that simplifies loop integrals by decomposing terms with linearly dependent propagators.
- Enhanced FeynArts integration and explicit support for color algebra with SU(N) generators make FeynCalc 9.0 ideal for complex quantum field and effective field theory computations.
Developments in FeynCalc 9.0: Enhancements for Quantum Field Theory Computations
The paper "New Developments in FeynCalc 9.0" discusses enhancements made to the FeynCalc Mathematica package, which facilitate symbolic semi-automatic evaluations of Feynman diagrams and algebraic expressions in quantum field theory (QFT). The improvements, particularly in version 9.0, are centered around tensor reduction, partial fractioning of loop integrals, interfacing capabilities with FeynArts, and support for color algebra involving explicit fundamental indices.
Major Improvements in FeynCalc 9.0
1. Tensor Reduction
A key improvement in FeynCalc 9.0 is the substantial enhancement of the TID function, which now supports tensor decomposition of one-loop integrals with any rank and multiplicity. It allows the option of using Passarino-Veltman basis for cases with non-zero Gram determinants, thus offering more compact expressions. The representation in terms of generalized Passarino-Veltman coefficient functions (GenPaVe) enhances the flexibility for users who prefer different conventions or need to express integrals with multiplicities beyond established libraries.
2. Partial Fractioning of Loop Integrals
The partial fractioning algorithm in FeynCalc 9.0 was built upon Feng's work and provides a comprehensive solution for decomposing loop integrals with linearly dependent propagators. This integration simplifies expressions without manual restructuring by decomposing integrals into terms with linearly independent propagators.
3. Improved Interface with FeynArts
FeynCalc 9.0 offers improved integration with FeynArts to generate and convert Feynman diagrams. Enhanced compatibility allows the merged use of both packages without conflicts, such as context mismatches arising from identical object names. The conversion and evaluation become more intuitive with the FCFAConvert function, providing refined control over the process, including momentum specification and chirality handling.
4. Support for SU(N) Generators with Explicit Indices
The introduction of SUNTF objects programs the SU(N) generators in their fundamental representations with explicit indices, allowing handling of amplitudes with more than two free fundamental indices. This resolves existing inconveniences in expressing multicolor interactions, thereby expanding FeynCalc's handling of color algebra.
Practical Implications and Theoretical Speculations
The developments in FeynCalc 9.0 illustrate a broader commitment to providing tools that accommodate the intricate demands of modern QFT computations. As a semi-automatic framework, FeynCalc complements more automated tools like FormCalc and GoSam by offering a tailored, flexible approach suitable for specific and complex calculations, especially in non-standard theories or models.
Its robustness is underscored in multi-loop processes and matching coefficient evaluations in effective field theories (EFTs), such as NRQCD. The adaptations for explicit non-relativistic expansions, demonstrated with high-level examples, suggest promising utilities in pedagogical environments and computations where such specific expansions are necessary.
Going forward, FeynCalc's direction may focus on enhancing multi-loop capabilities further, possibly integrating frameworks for numeric evaluation of higher-order loops or creating interfaces with additional computational tools to expand its applicability in cutting-edge research, such as in gravity and quantum chromodynamics at various scales.
The paper successfully demonstrates that despite increasing automation in QFT calculations, the demand for semi-automatic frameworks like FeynCalc continues, primarily due to their customizability and extensive suitability for specialized calculations. Consequently, as the computational scale of theoretical physics broadens, tools like FeynCalc will likely play a pivotal role, highlighting the interplay and integration of innovative and traditional computational methodologies.
