We study a class of renormalizable quantum field theories with purely virtual particles that exhibits nonrenormalizable behavior in the high-energy limit of scattering cross sections, which grow as powers of the center-of-mass energy squared and seems to violate unitarity bounds. We point out that the problem should be viewed as a violation of perturbativity, instead of unitarity, and show that the resummation of self energies fixes the issue. As an explicit example, we consider a class of $O(N)$ theories at the leading order in the large-$N$ expansion and show that the different quantization prescription of purely virtual particles takes care of the nonrenormalizable behavior, making the resummed cross sections to decrease at high energies and the amplitudes to satisfy the unitarity bounds. We compare the results to the case of theories with ghosts, where the resummation cannot change the behavior of cross sections due to certain cancellations in the high-energy expansion of the self energies. These results are particularly relevant for quantum gravity.
We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian classical limit, besides clashing with the observation of the muon. If, on the other hand, all the states are included, the LW models have a Hamiltonian unbounded from below or negative norms. Purely virtual particles, on the contrary, lead to a Hermitian classical limit and are ab…
Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity
We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics. The fake particle, or "fakeon", which mediates interactions without appearing among the incoming and outgoing states, can be introduced by means of a new diagrammatics. The renormalization coincides with the one of the parent Euclidean diagrammatics, while unitarity follows from spectral optical identities, which can be derived by means of algebraic operations. The classical limit of a theory of physical particles and fakeons is described by an ordinary Lagrangian plus H…
We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in arXiv:2111.11356 from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed $w_{1+\infty}$ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructibl…
We formulate a new quantization principle for perturbative quantum field theory, based on a minimally non time-ordered product, and show that it gives the theories of physical particles and purely virtual particles. Given a classical Lagrangian, the quantization proceeds as usual, guided by the time-ordered product, up to the common scattering matrix $S$, which satisfies a unitarity or a pseudounitarity equation. The physical scattering matrix $S_{\text{ph}}$ is built from $S$, by gluing $S$ diagrams together into new diagrams, through non time-ordered propagators. We classify the most general…
Using the ambitwistor string, we complete the list of celestial OPE coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet CFT to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to…
玻色化通常被认为是一种纯粹的二维现象，而一般的费米子在D>2的场论，除了在某些特殊情况下，是不能用局域玻色作用来描述的。指出在大N极限下，具有伴随费米子的R^{1，1} x S^{1}_{L}上的三维SU（N）规范理论可以玻色化.这些理论的关键特征是，它们对任意的圆尺寸L具有大的N体积独立性。其结果是这些3D规范理论和某些2D规范理论之间的大N等价性，其将3D理论中的一组关联函数与2D理论中的对应可观测量相匹配。作为一个例子，我们着重讨论了一种伴随Majorana费米子的三维SU（N）规范理论，并导出了大N等价的二维规范理论。额外的维度被编码在2D理论的颜色自由度中。然后，我们将非阿贝尔玻色化的技术应用到二维理论中，得到一个等价的局部理论，纯粹是用玻色变量写成的。因此，大N三维理论的玻色子化版本原来是存在于二维中的。
