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We investigate the mechanical structure of a spin-1 particle. Introducing three different frameworks, i.e., the three-dimensional (3D) Breit frame, the two-dimensional (2D) Breit frame, and the 2D infinite momentum frame (equivalently the two-dimensional Drell-Yan frame), we scrutinize the 2D and 3D energy-momentum tensor (EMT) distributions in these frames. We first derive the EMT distributions in the 2D Breit frame by performing the Abel transformation. The mass distribution in the 2D Breit frame contains an additional monopole contribution induced geometrically. The pressure distribution in the 2D Breit frame also gets an induced monopole structure. When the Lorentz boost is carried out, the mass distribution in the 2D infinite-momentum frame acquires the induced dipole term. Similarly, we also have the induced dipole contributions to the pressure and shear-force densities. We visualize the 2D mass distributions when the spin-1 particle is polarized along the x-and z-axes. We observe that the 2D mass distribution in the infinite momentum frame exhibit clearly the induced dipole structure when the spin-1 particle is polarized along the x-axis. We also discuss the strong force fields inside a polarized spin-1 particle.

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In this work, the electromagnetic and gravitational form factors of a spin-3/2 particle, ∆ resonance, are simultaneously calculated with the help of a relativistic covariant quark-diquark approach. The two kinds of form factors are separately extracted from the matrix elements of the electromagnetic current and of the energy-momentum tensor of the system. Our numerical results show that the approach can well reproduce the electromagnetic monopole, dipole, quadrupole, and octupole form factors comparing to the Lattice calculations. Our obtained electromagnetic moments are also comparable with some other approaches. Moreover, the obtained gravitational form factors, which give the mechanical properties of the system like the mass and spin distributions, are also displayed for the ∆ isobar. In addition, some discussions of the sign and the interpretation of the D-term are particularly given.