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Analysis Study Research Paper | Physics | Volume 15 Issue 4, April 2026 | Pages: 1066 - 1070 | India
A Complex Coordinate Approach to Relativistic Quantum Wave Equations: A Theoretical Analysis
Abstract: The present study explores a theoretical extension of relativistic quantum wave equations through the introduction of complex space-time coordinates. The motivation for this approach arises from persistent conceptual challenges in relativistic quantum mechanics, particularly those related to probability interpretation and particle localization. By reformulating the Klein?Gordon and Dirac equations within a complex coordinate framework, the paper examines how the mathematical structure of these equations can be broadened without compromising fundamental physical principles. The analysis shows that treating the wave function as an analytic entity in complex space-time provides additional flexibility in handling boundary conditions and singularities. It also offers a refined perspective on the interpretation of solutions, especially in cases where traditional real-valued formulations lead to ambiguities. The study further demonstrates that Lorentz invariance can be preserved through analytic continuation, ensuring consistency with relativistic requirements. Although the framework remains theoretical, it suggests that complexification of space-time may serve as a useful tool in addressing certain limitations of relativistic quantum theory. The findings indicate that this approach has the potential to contribute to ongoing developments in quantum field theory and may provide a conceptual bridge toward more generalized formulations of quantum physics.
Keywords: Relativistic quantum mechanics, complex coordinates, Klein?Gordon equation, Dirac equation, analyticity, space-time
How to Cite?: Dr. Abhishek Ranjan Singh, "A Complex Coordinate Approach to Relativistic Quantum Wave Equations: A Theoretical Analysis", Volume 15 Issue 4, April 2026, International Journal of Science and Research (IJSR), Pages: 1066-1070, https://www.ijsr.net/getabstract.php?paperid=SR26416220436, DOI: https://dx.dx.doi.org/10.21275/SR26416220436