Quantum field theory in flat spacetime with multiple time directions

Abstract

This letter serves as the generalization of the work 2505.16436, where we investigated the quantum field theory in Klein space which has two time directions. We extend studies to the general spacetime ${\mathbb{R}}^{n,d-n}(n,d-n\ge 2)$ in a similar manner: the ``length of time'' $q$ is regarded as the evolution direction of the system; additional modes beyond the plane wave modes are introduced in the canonical quantization. We show that this novel formulation is consistent with the analytical continuation of the results in Minkowski spacetime.

7 pages, 1 figure, 2 appendices; published version

References in corpus (31)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• The Kerr/CFT Correspondence
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• The BMS/GCA correspondence
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• On Tree Amplitudes in Gauge Theory and Gravity
• A holographic reduction of Minkowski space-time
• Holography of 3d Flat Cosmological Horizons
• Carrollian Perspective on Celestial Holography
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Gluon Amplitudes as 2d Conformal Correlators
• The S-Matrix in Twistor Space
• Bridging Carrollian and Celestial Holography
• Exploring the holographic principle in asymptotically flat spacetimes via the BMS group
• AdS Witten Diagrams to Carrollian Correlators
• $(2,2)$ Scattering and the Celestial Torus
• Classical Solutions and their Double Copy in Split Signature
• Uplifting AdS3/CFT2 to Flat Space Holography
• Holography in asymptotically flat space-times and the BMS group
• Celestial Amplitudes as AdS-Witten Diagrams
• Boosting to BMS
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• From Celestial Correlators to AdS, and back
• Celestial Leaf Amplitudes
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Diamonds in Klein geometry