实量子场论、J-量子化与标准模型
Real Quantum Field Theory, J-Quantization, and Standard Model
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中文总结 AI 辅助
研究提出基于实数的实量子场论（RQFT），通过用矩阵J替换虚数单位i构建，以标量场为例说明其满足相关方程和关系。RQFT与普通QFT物理可观测量一致，还探讨了标准模型的纯实表述及J对称性破缺对新物理的意义。
中文摘要 AI 辅助
我们提出一种完全基于实数的量子场论表述，即实量子场论（RQFT）。通过在所有公式中用矩阵J替换虚数单位i，从标准复数表述得到该构造，J是满足\(J^2 = -1\)的实2x2矩阵。这将基于实凯勒空间的实量子力学扩展到具有无限多自由度的系统。以标量场为例构建RQFT，定义作用于玻色福克空间实凯勒类似物的场算符，其满足克莱因 - 戈登方程和规范对易关系的J形式。为构建RQFT发展了相应的J - 演算，引入J - 傅里叶变换及相关J值分布。在RQFT中，复S矩阵的通常幺正性条件被实散射算符既是正交又是辛的表述所取代。RQFT的物理可观测量与普通QFT一致，不改变标量QFT的物理预测但提供等效表述。我们探讨基本粒子标准模型的纯实表述可能性，表明其确实存在且所得理论具有正交辛对称性。选择标准模型作为探索纯实表述可能性的测试平台，是因为它能现实描述所有已知基本粒子。标准模型的实表述自然暗示了超越标准模型的可能途径，特别是考虑将J对称性破缺作为新物理的标志。
英文摘要
We present a formulation of quantum field theory based entirely on real numbers, which we call real quantum field theory (RQFT). The construction is obtained from the standard complex-number formulation by replacing the imaginary unit i with a matrix J throughout all formulas. Here J is the real 2x2 matrix satisfying the condition J^2=-1. This extends the recently developed formulation of real quantum mechanics based on the real Kähler space to systems with infinitely many degrees of freedom. As the basic example, we construct the RQFT for a scalar field. We define a field operator acting on the real Kähler analogue of the bosonic Fock space. This operator satisfies the Klein-Gordon equation and the J-form of canonical commutation relation. To construct the RQFT we develop the corresponding J-calculus. In particular, we introduce the direct and inverse J-Fourier transforms and the associated J-valued distributions. In RQFT, the usual unitarity condition for the complex S-matrix is replaced by the statement that the real scattering operator is both orthogonal and symplectic. The physical observables in RQFT coincide with those of ordinary QFT. Thus RQFT does not change the physical predictions of scalar QFT, but provides an equivalent formulation. We explore the possibility of purely real formulations of the Standard Model of elementary particles. We show that it does admit this formulation and the resulting theory has ortho-symplectic symmetry. The choice of the Standard Model as the testbed for exploring the possibility of purely real formulations is related with the fact it provides a realistic description of all known fundamental particles. The real formulation of the Standard Model naturally suggests a possible exit beyond the Standard Model. In particular, we consider the implications of breaking the J-symmetry as a marker for new physics.
